precalculus

[torn pivot]

no

[viscid thistle]

6π too

[velvet sequoia]

The period is the shortest one

[torn pivot]

we take the smallest value as principle

[viscid thistle]

Oohh

does that mean, all period of trigonometric function is 2π??

[torn pivot]

No

[velvet sequoia]

sin cos sec csc have period 2π

tan cot have period π

[torn pivot]

2π*

[viscid thistle]

Aahh!!

[torn pivot]

you're in highschool?

[viscid thistle]

I only imagine there is only sin cos csc sec funtion lol

i forgot the tan cot

Lol

[velvet sequoia]

Now the amplitude

[viscid thistle]

Now the amplitude

ppfftt yeah

[torn pivot]

Now the amplitude

[viscid thistle]

Stop this chain lol, /jk

[velvet sequoia]

A wave has amplitude r if it has minimum height -r and maximum height r

[viscid thistle]

I see, in this case it is 3

[velvet sequoia]

Yup

[viscid thistle]

Am i correct?

So the function should be 3sin(2π)???

[velvet sequoia]

Not quite

Should be 3sin(x)

[viscid thistle]

Fuck

So what's the 2π for?

[velvet sequoia]

sin(x) itself already has period 2π

[viscid thistle]

Huh?

[velvet sequoia]

If it had period 20π, it would be 3sin(x/10)

[viscid thistle]

How the hell a function have a period 20π

[velvet sequoia]

Or if it had period 0.2 π, it would be 3sin(10x)

Multiplying a larger number next to the x makes it "oscillate more"

So that that's how the period is related

Since sin(x) already has period 2π, we don't need to multiply by anything (multiply by 1)

[torn pivot]

no swearing ✖️

[torn pivot]

By changing parameters of an elementary function

[viscid thistle]

Screw you >:( /just kidding

[velvet sequoia]

Here's 3sin(10x) for instance

[devout cove]

Is serge lang basic mathematics worth going through?

From doing the exercises in the first chapter, it seems like it wants you to prove a lot of things.

Is this continued throughout?

[paper tartan]

huh. I got a ping here?

someone's pinging me in these pre-uni math channels and then deleting their message

[hushed sphinx]

I've brought it up in the mod channel; it seems to be a user whose only activity is ghost-pinging.

[bleak jacinth]

Guys I'm taking AP precalc/trig (they combine it in my district) this upcoming school year - got any advice?

[last zephyr]

Going into make sure you are good at factoring

If you are wanting to study ahead of time ig you could learn trig identities and do work with those

Unit circle

Logarithms

Idk how people here feel about khan academy

But over the summer it couldn’t hurt to just go through that

[red wigeon]

Hey all! This isn't specifically homework help per se, but I was trying to follow this explanation and maybe my trig is just really rusty, but I don't understand how the tangent of the second angle is useful at all, especially not how it gets -h/a from that; furthermore I'm not positive why the tangent of the first angle would be a/h instead of h/a. I tried googling and I can't really find an answer that explains this, it's all talking about the core basics of trig, or else how to find a line perpindicular to a tangent using limits which also isn't what I'm looking for.

[hidden birch]

the tangent of the first angle is a/h because

\[\tan\theta=\frac{\text{opposite side}}{\text{adjacent side}}\]

[obsidian monolith]

glass

[hidden birch]

for the second angle, you can derive it when you take the tangent of 180° - second angle (supplementary angles)

[willow skiff]

search up the 'unit circle'

when we consider angles outside of the first quadrant, outside 0 to 90 degrees, we have to consider that each side can be negative as well as positive

so the side opposite to angle 2 is still h
but the adjacent side will become -a, because it's a units left

so h/(-a) which is the same as -h/a

[red wigeon]

What confuses me about that is, wouldn't that make it equivalent to delta x/delta y, making it run/rise?

[red wigeon]

Ah okay I will look at it again in just a few

[willow skiff]

if you rotate triangle CBD counterclockwise by 90 degrees

it actually does become rise/run

so rise/run isn't a good way of thinking about the tangent of an angle

tan is always opp/adj no matter the orientation

[hidden birch]

if you follow rise/run, it would actually be h/(line segment from A to D), not a. we have to check if h/AD segment would eventually be equal to a/h

[hidden birch]

i think south presents a better view of it

[viscid thistle]

I’m g8 and is it possible to learn calculus?

[willow skiff]

yes, provided you have the right algebra and geometry fundamentals

here's a playlist: https://www.youtube.com/playlist?list=PLHVJy2PpMfJb7kj1QESOVlWcf1vyQeNWL

[viscid thistle]

Ok thanks

[willow skiff]

https://www.youtube.com/watch?v=TzDhdvVg9_c

I also found this video pretty amusing

if you want a textbook to practice, use James Stewart's Calculus : whatever edition is fine

or on LibreTexts there's also plenty

[willow skiff]

no worries!

[bleak jacinth]

Yah that's where I'm learning chem bc my friends are taking it over the summer and I couldn't

[rare sparrow]

why is there no calculus channel for pre uni?

dont most highschool students learn calc

[torn cove]

im suffering in these questions of mine. And i cant find any help online as i keep on getting different answers

you guys wouldn’t be able to help me, would you 😭🙏

i got 0 on a and its really bothering me

[strong storm]

@torn cove

First notice, the green line is the secant line (touching two points) that passes through (f(a),a) and (f(b),f(b))

The slope of the green line can be found out using rise/run, and this slope is the average rate of change of the function in the interval [a,b]

[last zephyr]

lmk how your journey with precalc goes

[hushed sphinx]

There is one #calculus channel that is for calculus no matter where and when you're taught it.
The calculus channel is in the "Early University" section because that is where most Americans learn the topic, but that doesn't change the fact that it's the topic that defines the channel content, not its location in the channel list.

[neon steppe]

Is there a way I'd be able to understand why the domain of fog is a subset of domain of g in an intuitive manner?
Specifically why it's only true for g 👀
fog's domain isn't necessarily a subset of f's domain?
Why does only the inner function matter?

[hidden birch]

because the domain of f is the range of g

y=f(g(x))

imagine g(x)=x². Then the domain of f will only be ≥ 0

[willow skiff]

if there's some number that you can't put into the function g, because g(x) will be undefined

then f(g(x)) = f(undefined) = undefined as well

there could be other inputs that make f(g(x)) undefined, where g(x) is still defined

so like if we take g(x) = 2x and f(x) = ln(x)

g(-1) = -2 is defined
but f(g(-1)) = f(-2) = ln(-2) is certainly not defined

[neon steppe]

Hmm 👀

[hidden birch]

,,\to\boxed{g(x)}\to\boxed{f(x)}\to

[obsidian monolith]

glass

[hidden birch]

,,\gets\boxed{f(x)}\gets\boxed{g(x)}\gets

[obsidian monolith]

glass

[hidden birch]

it's roughly like g's y-axis reused as f's x-axis

[neon steppe]

Thanks ✨
I believe I get it now, dom(fog) is the domain of (g) removing the values of x for which g(x) inside f(x) is undefined 👀

[hidden birch]

therefore f's domain is a subset of g. f's domain can be at least equal to g's but never a superset of g

[neon steppe]

Yep, thanks ✨

[hidden birch]

sone elements of domain of g could also have the same output, decreasing what it feeds to f for its domain

[willow skiff]

so we basically have this scenario

there's numbers inside the domain of g that still make fog undefined, so that would be in the blue circle but not the green circle

no worries!

[regal tree]

damn this is such a nice way to explain this

[willow skiff]

if there's some number that you can't put into the function g, because g(x) will be undefined -> then f(g(x)) = f(undefined) = undefined as well

call the green set G and the blue set B

then $B' \subseteq G' \implies G \subseteq B$

and the other part shows that both sets are not the same size, so f compose g must be a proper subset

[willow skiff]

np!

[regal tree]

just thought of an example:
Say g(x) = x^3
and f(x) = lnx
now g(x) is defined for all real numbers but fog(x) is only defined for x>0

[willow skiff]

https://www.youtube.com/watch?v=xuy27ueM4OE

[obsidian monolith]

south

[neon steppe]

Thank you 🙏🏻✨

[willow skiff]

np again!

[bleak jacinth]

Only those who want to and go ahead - you'd be surprised, my high school district usually has people learn Algebra I freshman year

[bleak jacinth]

will do

[noble lava]

you can go to id:customize and tick #calculus if you want

[rare sparrow]

im not from USA so idk how it works there but everyone in my school atleast knows basic calculus no matter what math course they choose

[bleak jacinth]

That would be nice. But my school is what some would describe as "ghetto-like" and it'd be a miracle if anything like that happened here.

[silent plaza]

I don't get the draw the secant line, so you are supposed to do approximations with secant line or what?, or it just means that you have to find the derivative and draw the tangent line at given point?

[willow skiff]

no, the average rate of change is not the derivative

it's the slope of the line that passes through the two endpoints, so the slope of the secant line

my guess is that drawing the secant line helps you spot calculation errors

so if the secant line is clearly increasing, but you get the average rate of change is negative, then you must have made a mistake in your calculations

[willow skiff]

so through (a, f(a)) and (b, f(b)) the slope would just be (f(b) - f(a))/(b - a)

[silent plaza]

Ahh, so you don't use limit on this one, it just, you have to pick two points for secant line?

[willow skiff]

exactly

[mortal harbor]

Hi, is anyone taking calculus with business and social science applications to include polynomial, rational, exponential and logarithmic functions and their graphs; multi-variable calculus to include partial differentiation, optimization, and introduction to differential equations.

Math 165?

[willow skiff]

not here, go to to #calculus

[golden basin]

Here x>1 only or x>1 + x<5?

Find the values of x satisfying the following inequalities and graph them on
the number line.
(x − 1)(x + 5) > 0

[whole island]

the idea when solving inequalities such as this is to determine the intervals, or areas, that make it true..

you have your roots, pick different just one number from each of the areas surrounding your roots and plug them into the inequality to determine the interval(s) that make it true by getting an output that satisfies it

(blue representing the plotted roots, green representing the test numbers, f(x) being your function (x-1)(x+5) with x being the tests)

[golden basin]

got it

thank you

[desert thorn]

guys if you dont mind me asking do you have any recommendations for any youtube videos for an introduction and course for calculus, i need to learn integration and diffrentiation for my additional maths course so i thought it might as well be worth it to learn it fully in depth

[cedar geyser]

Most people use organic chem tutor for calc i think

Also khan academy maybe

[kindred jasper]

hi sorry if this isnt the right place to ask but is there a calc channel

or is this one used for that too

[hushed sphinx]

#calculus ?

You may need to check the "show all channels" box in the context menu that drops down from the server name.

[kindred jasper]

ohhh okay ty!!

[odd coyote]

is anyone doing the precalculus course in silicon valley hs?

[nimble wolf]

no, but I'm about to take Precalculus course at AOPS soon...

[willow skiff]

You're looking for a needle in a haystack

Granted there are quite a few people who might go to some kind of online school, but even still...

[warm yoke]

i took algebra 2 online through a similar program

[limber frost]

Can I self teach calc bc while taking precalc in school or is that not rly feasible

[shy vine]

yeah I think its possible

[uncut mulch]

depends how well you're doing with precalc content

as calc builds on that
without that foundation, you'll constantly be slowed down by knowledge gaps

[eager forge]

How can I draw a parabolic bridge

[hushed sphinx]

First, what do you mean by "parabolic bridge"?

(If you don't already know what you mean by it, we need to see more of the context you found the phrase in).

[cold monolith]

Thanks to the individual helpers on this server for helping me answer the question of how to calculate the Vishwanath's constant

[cold monolith]

Check out what I got

[next condor]

Pre cal killing me🥀

[bold edge]

What do you pearn in precalc

[tawny flint]

Hey guys, I’m going into 9th grade and I’m planning to take Alg 2 trig at school, and do pre calc honors simultaneously outside. Any recommendations on good pre calc honors courses/tutor/anything lol.

[mortal helm]

I'm in 10th and with this I'm in pre calc, so I would recommend the usage of Khan academy.

[tawny flint]

So ur saying that it would be good to just self study pre calc using khan academy?

[willow skiff]

don't just use Khan Academy

get a book as well to have everything in one place as well as for longer and more in-depth questions!

I recommend Axler's Precalculus but James Stewart's Precalculus is also quite good

[coral crow]

Look up Professor Leonard on yt. He has a really good playlist on precalculus.

[spare pier]

somebody tutor me w this i cannot learn math by reading

[molten slate]

anyone here read or is reading the book "Basic Mathematics" by Serge Lang

[modest bolt]

do you know about greatest integer function?

[spare pier]

im showing you it here

😭

[modest bolt]

Nah, I mean this image isn't defining the function. It's assuming you have read about it before and telling about the limit of the function.

[spare pier]

oh

no i dont

[modest bolt]

Greatest Integer Function(GIF) or we can say the Floor Function, another name of the same function is defined as
int x = greatest integer less than or equal to x

Examples:
int 4.4 = 4
int 4=4
int 0.00000001 = 0
int -1 = -1
int -0.1 = -1

[spare pier]

the last exmaple?

was it supposed to be -1.1

[modest bolt]

-1 is the greatest integer less than or equal to -0.1

-1.1 is not an integer

[spare pier]

😭

ohhhohh

no i mean

[modest bolt]

you have to look for this

• Which is the nearest INTEGER <= x

[spare pier]

int -1.1 = -1

?

[modest bolt]

-1 is greater than -1.1

I said greatest integer LESS THAN or equal to x

in negative numbers -2 < -1

I understand this is confusing for negatives

[spare pier]

so it cant just be 0

-0.1

[modest bolt]

0 is greater than -0.1
I want a y such that

1. y is integer satisfying y<=x
2. and y is nearest to x

[spare pier]

okay

[modest bolt]

look for these 2 conditions

int -0.1 = ?

1. ? <= -0.1 and ? is integer
   → ? can be -1, -2, ....

2. ? is nearest to -0.1
   → ? is -1

[spare pier]

i gett itt

[modest bolt]

you know the BEST method to do this? imagine the number line and plot x on it, now the first integer you get moving left from x is GIF of x

[spare pier]

huh does this work if its like 4.5

[modest bolt]

got it?

yes

[spare pier]

then its 4 no?

[modest bolt]

what's int 4.5?

[modest bolt]

yes

[spare pier]

yayayaa

okay

what abt 4.6

😭

[modest bolt]

now look at this graph.
you see that for 0<=x<1, if you plot any these numbers on number line and go left, first integer is 0.
Hence GIF of all x from 0 to 1 = 0 which is shown here

[modest bolt]

4

[spare pier]

wait let me

ok

[spare pier]

then what about 4.9

4?

ITS 4?

[modest bolt]

yes

[spare pier]

ITS SO CLOSE TO 5 THOUGHJ

[modest bolt]

doesn't matter

that's what's special about it

tell me int 5

[spare pier]

5

[modest bolt]

good

so do you see that for any integer n, if you take any number in [n, n+1), you get it's int = n

[spare pier]

ohhh

OHHHH

[modest bolt]

you understand this?

[spare pier]

no i dont understand that

i was saying ohh for the graph

i finally get the graph now

[modest bolt]

oh

[spare pier]

😔

[modest bolt]

replace n with 4 here and then try and also to you know what [n, n+1) represent here? it's a set notation

[spare pier]

i havent learned set notation yet

[modest bolt]

your school started limits without sets?

[spare pier]

i think i get the basis

[spare pier]

i havent started school yet

im doing this class to prep for calc

calc ab

[modest bolt]

yea but yk your basics aren't very clear

[spare pier]

wow

what doy uommena

set notation i know union

[modest bolt]

I mean you are supposed to know about Sets and GIF before moving to limits.

they are part of pre calc

[spare pier]

what actually

i took honors precalc and they didnt have it in the curriculum

[modest bolt]

well if you haven't learnt that yet, np. I will try to have you understand the graph without those

[spare pier]

im just trying to learn it so i can just solve a few math problems that he assigned to me but his teaching is booty 😭

[modest bolt]

so you see what it's trying to say is that if you take any INTEGER say n and take any real number very close to it on its right, say x and take its GIF, then int x = n.

for example, take 4 and a number on its right very close say 4.000001 then int 4.000001 = 4.

Now I hope you know what is limit at a point. So when finding right hand limit of GIF of any integer, you get the integer itself back. So, Right hand limit of int x at x=4 is 4

[spare pier]

i get that

i understood it a few minutes agooo

[modest bolt]

reminding that i am telling you only about what that image is trying to tell and not teaching you to solve limits problems

[spare pier]

😭

about the image

what is up with the equation

[modest bolt]

now what if you take left hand limit of GIF of any int? what's LHL of int x at x=4?

[spare pier]

isnt it 4 😭

[modest bolt]

do you know that left hand limit means taking a number very close to x on left side of x? means you are trying to find int 3.99999

[spare pier]

no

yes

no

im not understanding the left and right

[modest bolt]

Have you not learnt about how to find limit of f(x) at any x?

[spare pier]

i learned a bit

😭

[modest bolt]

ngl i m about to quit like this

[spare pier]

lend me some patience

i do better at seeing someone solve limit problems and then actually learning the concept from it 🥺

[modest bolt]

can you tell me what kind of questions your teacher gave you

[spare pier]

only 2 of these problems are my homework but just do one

or two 🥺

[modest bolt]

oh, now
lim x→k+ int x
means int of a number very close to x on its right side

lim x→k- int x
means int of a number very close to x on its left side

[modest bolt]

try 1st,

[spare pier]

me

[modest bolt]

what is int of a number very close to 0 on its right

[spare pier]

0.1

OH

[modest bolt]

it's int

[spare pier]

1

[modest bolt]

you forgot what i said, plot it and move left

[spare pier]

youuuu saiiidd on its righhtt

[modest bolt]

first integer you encounter is its int

[modest bolt]

I said int of a number on right of 0

so suppose 0.01
int 0.01 = ?

[spare pier]

😔

[modest bolt]

.

what's int 0.01 ? means what's GIF of 0.01?

[spare pier]

isnt integer a whole number

[modest bolt]

integer means ...-2, -1, 0, 1, 2....

[spare pier]

yess whole numberss

[modest bolt]

no integer is not just whole number

whole numbers are 0, 1, 2....

integers means including negatives as well

[spare pier]

okay

[spare pier]

so is 0

[spare pier]

0

?

[modest bolt]

ok let me do 1st for u

lim x→0+ int x

1. "+" means find a number closer to 0 on its right, so I take x=0.1
2. now, I am asked to calculate it int x = int 0.01.
3. i know for int x, i plot x then move left and the first integer i encounter is the int x
4. hence int 0.01 = 0

now do 2nd

[spare pier]

wait

let me do 2nd

okay

ITS -1

[modest bolt]

yes

[spare pier]

BOOOOM

[modest bolt]

3rd?

[spare pier]

is just 0?

[modest bolt]

ok leave 3rd

[spare pier]

is 3rd 0

[modest bolt]

i haven't told you for lim x→k without any + or - in it

so leave 3rd

tell me others

[spare pier]

okay

40. is -3

yes

or no

[modest bolt]

how did you get -3??

[spare pier]

😭

[modest bolt]

no

what did you do there

[spare pier]

i move left

[modest bolt]

think like this

tell me what number you got from 1

[spare pier]

i move to 2.1

-2.1

[modest bolt]

it's "-" not "+" in 40

[spare pier]

int -2.1

[modest bolt]

so you find a number left of 2

= 1.9

[spare pier]

omg

[modest bolt]

• → right of 2
  - → left of 2

now try

[spare pier]

omg

its -1.9

left of 2

its -2 though

OH

OHH

WAIT

[modest bolt]

🦆 why -1.9?? left of 2 you get +1.9

[spare pier]

I thought of it as -2

😔

[modest bolt]

no it's +2

now tell

fast pls i am leaving

[spare pier]

okay

then is it 1?/?/

😭

yes or nooooooooooooooooooooo

[modest bolt]

yes

next

[spare pier]

yipe

01

wait

what is this

[modest bolt]

you know |x|?

mod of x

[spare pier]

its absolute value

[modest bolt]

yes that

[spare pier]

its 0.1/0.1

[modest bolt]

do 1st step same, just from there you know that you have to calc x/|x| value for the x you got in 1.

[spare pier]

its 1

[modest bolt]

yes

[spare pier]

okayokay im pro now

[modest bolt]

last

[spare pier]

next -0.1

is

-1

yes no

-0.1/0.1 is -1

wait im getting the hang of it 😔

[modest bolt]

for 39. If you are asked to find lim x→k int x without any + or - you have to do this

1. Is lim x→k- int x = lim x→k+ int x = int k?

• If yes, then lim x→k int x = int k.
• If no, then lim x→k int x doesn't exist.

[modest bolt]

yes

[spare pier]

oh so i have to find it both ways

yes or no?

[modest bolt]

yes

[spare pier]

okay

[modest bolt]

before going tell me 39 answer

just to tell you that when you try to find close number on right of 0.01, you will take something like x=0.011 or x=0.02 because you want a number very close to 0.01 on its right

[spare pier]

left is 0 right is 0.02 i plug them in and i just get 0?

[modest bolt]

similar for when you try to find for close number x on its left

[spare pier]

oh

o

[modest bolt]

Answer is Right congro

[spare pier]

wait i cant use 0?

[modest bolt]

but remember to take a number very close

[spare pier]

okay

[modest bolt]

for left you have to take 0.009

though answer will be same

[spare pier]

okay

YAAYYA

thank you

[modest bolt]

welcome

[spare pier]

so much

[modest bolt]

gonna complete Astra lost in space now

[paper tartan]

@spare pier unrelated, but welcome to the mathcord!

[paper tartan]

Axler has a precalc book? :o

oh, he does!

I did not know this

[spare pier]

😭

[paper tartan]

apologies

[spare pier]

cannn

yoouuu

wallkkk througghh with meeee withhh thiis

sdiiiiiiii

[fading tundra]

what are you stuck on?

[devout bone]

i have absolutely 0 knowledge about multivariable limits but i wanna know if smth like L'Hôpital exist for multivariable limits?

[spare pier]

JOYCE

[spare pier]

i get it now😔

[fading tundra]

AHHH NICE!!

sorry i was in a tennis lesson 😭

[chrome sonnet]

precalc makes me wanna kms

[simple moss]

whats the part that confuses you about this

[crystal idol]

is precalc hrd

[stone urchin]

precalc is ez

[winged epoch]

So I understand how the distance formula is derived from Pythagorean theorem, but I’m wondering why it cant just be (x_2 -x_1, y_2 -y_1) which would give the length of the line which is the distance between the two points

[magic sequoia]

Usually you want the distance to be a real number

(x_2-x_1, y_2-y_1) Is not a real number

The length of the vector (x_2-x_1, y_2-y_1) does give you the distance between x and y though

There are other valid ways to define distance between two points though

[sonic fiber]

daddy

[marsh stag]

I'm not sure if this is the right channel

But could someone explain Vietas formulae for an nth degree polynomial?

And how I could prove them?

Thanks!

[nimble wolf]

Here's an image that I found on Google about Vieta's Formulas....

[regal tree]

we were really taught these and used them for years without knowing what they are called lmao

veita's formula damn

[marsh stag]

Thanks!

[whole void]

rlly?

[willow skiff]

"sum and product of roots" is a perfectly acceptable name

Vieta's is just shorter, and thus more convenient

[mild canopy]

man when I first see 'vieta's formula' I think of ones for quadratic equations

[long tapir]

Why is the answer to this -8 and not just 8?

[uncut mulch]

how are you getting 8

[long tapir]

I end with lim x -> 17 4 + sqr(x+1)

[willow skiff]

the square root only has one value

any function which has more than one y-value for every x-value is not a function

by convention, we always choose the positive square root

[echo sinew]

Mmh I don't think this is the problem

[uncut mulch]

can you show your work

[willow skiff]

ah wait, you should get -4 - sqrt(x + 1)

[echo sinew]

He just forgot a minus sign after simplifying

[long tapir]

It’s the bottom one

[uncut mulch]

16 - x + 1 isn't x - 17

[willow skiff]

<@&268886789983436800>

[echo sinew]

<@&268886789983436800>

[uncut mulch]

dw, i'm right here 🙂

[nimble wolf]

Oh yeah same here lol. Vieta's Formulas works for any polynomial of nth degree

[willow skiff]

fast as lighting, kung fu fighting

||you're also a little bit frightening /jk||

[long tapir]

Ah mb mb must have overlooked that mistake

[mild canopy]

Thanks for sharing those

I didnt cover those in school yet but I learn at home as much as I can

[willow skiff]

also you can make a free account on Brilliant.org

then you can access wiki pages like https://brilliant.org/wiki/vietas-formula/

[mild canopy]

Thought its paid

Didnt know they had a free plan

I study EE (im in technical high-school rn) but I love to study other concepts and math+physics below just normal curriculum

[willow skiff]

you can't access any of the paid courses

but yeah they have some stuff in the free plan

[mild canopy]

I'll check it out thanks

[chrome acorn]

use l-hoptial

[nimble wolf]

Yeah me too.

[uncut star]

Is this telescopable or solvable through elementary methods(precalc knowledge)
1/1.2.3 +1/4.5.6 +1/7.8.9 ...

[regal tree]

im not sure if it will work but try spliting the general term into partial fractions

[whole void]

Very likely not

cause it apparently converges to

$\frac{1}{12} ( \pi \sqrt{3} - 3 \log 3)$

[obsidian monolith]

hockeydude85

[warped shuttle]

L’Hopital your way through

[marsh stag]

L Hospital

[graceful inlet]

I am taking pre-cal this year.. Any tips?

[marsh stag]

I'm not sure

[uncut star]

i was unable to find any solutions online

[nimble wolf]

You'll be great, if you just practice the concepts before 🙂

[whole void]

https://math.stackexchange.com/questions/573119/how-find-this-sum-sum-limits-n-0-infty-frac13n13n23n3

[warped shuttle]

When did it become hospital

[hidden birch]

-# i think the letter ô used to be a short way of writing os back then by scribes?

-# > French: "ô" can represent a long "o" sound or indicate the historical loss of an "s" (e.g., "hôtel" was originally "hostel").

[true geode]

implication's more the other way around then

[smoky ridge]

anyone preparing for jee

[regal tree]

me!

[smoky ridge]

from where

[regal tree]

Pace

[nimble wolf]

well, I'm solving a few JEE questions (in Math) as a 9th grader now lol.

Also, I was wondering if anyone is going to take (or taking currently) the AoPS PreCalculus course.... if yes, how do you find the difficulty? I think it's going to be quite hard.

[robust sun]

ig, L hospital is not required , he should rationalize and then simpley solve to a point where limit can be applied

[paper tartan]

@smoky ridge welcome to the mathcord c:

[true geode]

Yes, if you rationalise this, you can get a fraction that doesn't need l'Hôpital to evaluate the limit

[warped shuttle]

Ofcourse but L’Hospital is faster

[hard stag]

Hi, is this correct?

[willow bear]

your original thing was

(3+2i) * (4-2i) * i

right?

[hard stag]

Yes

[willow bear]

ok then you made multiple mistakes

[hard stag]

Well it was (3+2i) * (4-2i)

But i think it's the same

[willow bear]

was there an extra i multiplying it, yes or no?

[hard stag]

No, te original is (3+2i) * (4-2i)

And to solve it I add the i because of the formula

[willow bear]

ok then you hallucinated the extra i

you tried to do 2 things at once:

• apply the formula
• distribute the honest way
  and you duplicated a bunch of things

you have to do exactly one

tell me here and now, which one do you want

[hard stag]

I want the most solid way, so the formula

[willow bear]

ok sure

(3+2i)(4-2i)

then:

• a = 3
• b = 2
• c = 4
• d = -2

[hidden birch]

that formula is supposed to be the result of (a+bi)(c+di)

[willow bear]

• ac - bd = 3*4 - 2*(-2) = 12 - (-4) = 12 + 4 = 16
• ad + bc = 3*(-2) + 2*4 = -6 + 8 = 2

(ac-bd) + (ad+bc)i = 16 + 2i

[willow bear]

key point is this

b is 2 not 2i

b is the number attached to the i but it does not include the i inside of it

likewise d is -2 not -2i

@hard stag

[hard stag]

Ok, tysm!

[hidden birch]

,texsp||algebraically,[(a+bi)(c+di)=(ac-bd)+(ad+bc)i]||

[obsidian monolith]

glass

[hard stag]

So the formula is incorrect?

[hidden birch]

the formula is the result formula, it seems

[willow bear]

who said it was incorrect

[hard stag]

So it only applies to prove if the result is correct?

[willow bear]

?????? what are you talking about

[hard stag]

I don't know if there's a problem using that formula

[hidden birch]

do u know the foil method?

[hard stag]

No

[hidden birch]

do u know how to multiply binomials?

[hard stag]

Yes

[hidden birch]

here's an exercise for you: multiply the binomials a+bi ans c+di

[hard stag]

What is ans?

[hidden birch]

the point of the exercise is to give you insight on how it is done

[hidden birch]

do it first then let's compare answers later

do it on paper

[hard stag]

Without using the formula, like I believe it's the honest way: a(c) + a(di) + bi(c) bi(di)

[hidden birch]

what is i×i (i is the imaginary number √(-1))

[hard stag]

ixi = i^2 = -1

[hidden birch]

can you please simply the answer further?

[hard stag]

I'll try

[hidden birch]

(if you can)

[hard stag]

I've tried my best haha, sorry if it's horrible

[hidden birch]

the way u factor out is incorrect

but anyway

i just wanted to point out that bidi is -bd. Can you see why?

I'm losing energy

[hard stag]

No, I see -b-d

[hard stag]

Np, ty for helping

[hidden birch]

i heard khan academy is good for learning math. i haven't tried it myself tho. maybe you should try it

[hard stag]

idk, I'm studying by my way with a book and yt videos, i'll see khan academy

[hidden birch]

sorry i meant you

i think that kind of math you're studying can be mastered with much practice

dude ur discord acc is old. how old were u when u made it

[hard stag]

I have an important exam the next year, like in May, and I have to learn 2 entire courses by my own, the 17 and 18 yo courses, in Spain 1bachillerato and 2bachillearto

[hard stag]

idk, a few time ago hehe

Im 19yo actually, so when I did it I was 11 or something like that

[hidden birch]

i hope you pass

[hard stag]

Ty!

[hidden birch]

,align bidi&=iibd\
&=-bd

[obsidian monolith]

glass

[hard stag]

If the order doesn't affect the result why we move them?

We move them, the ressult is different, and that's the correct result

[hidden birch]

for emphasis only. it's the same by the commutative property of multiplication

[hidden birch]

how is it different

[hard stag]

Ahhhh ok

Now I see it ty

[hidden birch]

,align bidi&=b\cdot i\cdot d\cdot i\
&=i\cdot i\cdot bd \
&=-1\cdot bd\
&=-bd

[obsidian monolith]

glass

[hidden birch]

-# i hope noone sees this and mentions ||ski||bidi

[hard stag]

Ty both! I could do again the exercise this time correctly and understand it better!

[hidden birch]

Also the way you factored out $a$ here is incorrect.
\begin{align*}
ac+adi &= a\cdot(c+di), \text{not } 2a+cdi
\end{align*}

[obsidian monolith]

glass

[hard stag]

True, ty

[hidden birch]

idk how u arrived at your answer. But u can always work backwards from the answer to the original problem to see if u actually did it right

Distributive Property

,,a\cdot(b+c)=ab+ac

[obsidian monolith]

glass

[hard stag]

Yes, idk how I did that factorisation haha

Ty for the help @hidden birch

[winged wigeon]

-# i was going to say what the skibidi

[celest fiber]

.

[crystal idol]

im a 8th grader going to 9th and im going to take precalc but im wondering if i should take precalc honors. any advice?

[idle field]

When are you going to take that class?

[crystal idol]

Coming school year

[idle field]

hmmm

I think it's a bit early

but if you feel comfortable with it, why not

I'm not familiar with the honors classes from the US, and I took calculus a long time ago, so try solving as many exercises as you can. That's my advice.

[sweet kindle]

What the

[coral wedge]

imo pre calc isn’t all that bad, so I’d take honors

solid GPA boost and you’ll be more prepared for calc

I’d assume taking pre calc as a freshmen means your really solid at math

so honors should be fine

[willow skiff]

it might motivate you more if you're able to get exposure to why the ideas behind calculus are true

meaning that in addition to regular functions, trig, sequences and series, and possibly matrices

this work might get extended to Riemann sums (working with summations) and the difference quotient

as you take the width of the rectangles in the Riemann sum to 0, or take h to 0 in the difference quotient, and find the resulting limit

boom! you've just done calculus, from the ground-up

I find that (subject) acceleration, which is covering material at a higher grade level or a faster pace compared to your peers can really help you figure out if maths is for you, at uni or as a career

if you feel motivated by learning all these new concepts, great!

but equally if you feel that you're being pushed or dragged, then that's okay too, cause it's better to find out sooner rather than later what you like and what you don't like

[ripe field]

south can i dm you for math advice

[flint blaze]

i love math

[noble lava]

pog

[nimble wolf]

PreCalculus = Awesome 😎

[noble lava]

pog

[willow skiff]

no, pls don't

but thanks for asking before you DM

[ripe field]

😔

[warped shuttle]

Is this a valid proof ?

[echo sinew]

Yep, perfectly fine

[warped shuttle]

Is this a “better” proof than the algebraic one?
x= 0.9999
10x=9.9999 and so on

[hushed sphinx]

Yes.

The multiply-by-ten argument assumes that you already know that analogues of the standard decimal arithmetic works for infinite decimal expansions, and establishing that requires a fair amount of limit manipulation itself.

[crystal idol]

@willow skiff @coral wedge thanks for the advice 🙏

[lethal sand]

it depends on your teacher my hpc teacher freshman year was really bad so the class was a nightmare

[warped shuttle]

How to find b such that the equation only has one real solution?
-16x^4 + 7x^2 -2bx - b^2

[willow bear]

this isnt an equation so theres nothing to solve

did you mean: -16x^4 + 7x^2 -2bx - b^2 = 69?

@warped shuttle

[warped shuttle]

Oh sorry I forgot the equals zero part

-16x^4 + 7x^2 -2bx - b^2 = 0

[willow bear]

ok

any progress so far?

[warped shuttle]

Not quite i don’t know how to deal with quartic equations that much
All i know is it’s a depressed quartic as we don’t have x^3

There was a ferrari method of solving these but don’t know how to use it to find b such that it has 1 real solution

[willow bear]

yeah i dont think you will be doing this in a 100% algebraic way

one insight that i can see immediately is that your quartic will need to have a double root

let f(x) = (your LHS)

if there's any hope of f having exactly one real root, this root will need to be shared with f'

[warped shuttle]

Alright thanks i will see if I can do something with it

[rustic badge]

Or sth like 1/3 = 0.333333 so |*3 is 3/3 or 1 = 0.999999999

[echo sinew]

I prefer the one you did honestly, it sounds more rigorous

[safe star]

if anyone can help me out here, i would much appreciate it. i have a help forum posted thats related if anyone wants to look at the original question but if someone could, recommend me a path to take to learning precalc? i know geometry and algebra 1 and am taking algebra 2/trig. dont dip on me like the last guy!

[whole void]

wdym? Just finish alg 2 and ur ready

[hybrid roost]

to my knowledge, precalculus is composed of trigonometry and algebra 2 (specifically college algebra types) if you study those ur good

[safe star]

ah... okay 😭

[hybrid roost]

guys, i need your advice, i am overthinking and overwhelmed, im taking ap precalc next year and i picked out a textbook that i want to self study but i dont know how im going to be able to self study because the current education system for my school is just giving math paper packets until you drill the material into your head, and also the textbook i picked out (stitz zeager precalc 3rd ed) doesnt align with ap precalc at all, it starts from types of numbers and works its way up

[hard needle]

You are planning to self-study the course that you're going to be taking next year? Why? If it's just to get ahead and get extra practice, anything you send study will help, so just working through the book you have will be fine.

[whole void]

yeah working up from types of numbers is kinda odd for precalc. ap precalc isnt rlly difficult imo, especially since there are only like 3 units

[hybrid roost]

i prefer note taking over paper packets

i cant learn with paper packets

[random widget]

What is chain rule?

[hybrid roost]

its a nightmare

[whole void]

if u find a good textbook, thats all u need then right

[hybrid roost]

not exactly that easy, its gonna be a lot of self study, but im thinking of taking sections from it and aligning it with the units

ill see how life turns out, it cant be exactly too difficult to do any of that on my own

[fading scarab]

Hello guys, I am trying to self study Calculus BC so I can do the test at the end of the year, but I am in precalc and my school is yet to start. What will I need to know about precalc (likely mostly trig) in order to be able to do this? I am quite enjoying doing calculus but I am stuck currently with tons of rules about sin cos and tan that I have never learned

[hybrid roost]

I think trigonometry. If your algebra foundation is weak, that would be a very big problem. But if you master trigonometry, matrices, (which is college algebra) and a few more stuff you are good to go.

like try to compare what you know to ap precalculus

[idle field]

Is matrix college algebra in the US?

[fading scarab]

okay thank you, I would say my algebra is pretty good

[willow skiff]

Usually they skip matrices so that students can progress on to calc 1 with more relevant foundations

That's the difference between the same course in HS and at a remedial level

But it really depends on the particular uni

Complex numbers is also fairly commonly included

[willow skiff]

Or you might get Gaussian elimination, representing systems of equations in matrix form
But then students don't know how to calculate a 2x2 inverse

So yeah it really depends

[willow skiff]

The issue is how you can even assume anything when there's no national standard
When the prof can adjust the course according to the ability levels of their students, so the prof can go "right, there will be no matrices on your final"

It's not like at high school where they're teaching to the AP tests

Not to mention the college algebra curriculum is extremely bloated, even at the pace of college

[random widget]

Hello guys I need a cheat sheet for precalc I’m in igcse year 1/ grade 9 can someone share it as I’m giving precalc and calc ab this year

[echo sinew]

I think there's plenty on the Internet

[willow skiff]

really? you're taking those externally right cause you're only in IGCSE grade 9

IGCSE for those who aren't familiar is only around algebra 1 level, with basic trig, descriptive statistics, and coordinate geometry

[faint sail]

Guyss what's the best method to get used to the flow of solving?

Do I have to repeatedly solve?

😢 where do I even start?

[hasty crown]

of solving what?

[willow skiff]

exactly..... we need to know what question(s) you want to do

[abstract kindle]

Heeyy! Im not the only trans girl here thats great to know :3

Hihi :3

[hasty crown]

hello

theres alot of us here

https://discord.com/channels/268882317391429632/1160361906536710265

[abstract kindle]

Omg thanks so much for showing me that chat, i always feel more comfy when many of us are around

I must join my people >:3

Didnt expect a math server lgbt friendly or not to have many of us here

[hasty crown]

math is very gay

[abstract kindle]

I have not been made aware of this fact x3

[slender harbor]

Develop this idea

[hasty crown]

theres just alot of gay people in math

[slender harbor]

Ok solid argument

[abstract kindle]

I've been studying math for 5 hours and the hell of it is I actually like it.

If my younger self heard me say that they would call me an imposter used to hate math but it just come so easily now that I'm older

The only reason I'm stopping is because my brain literally can't handle anymore without a break

Decided to come in here a little bit worried I'd have to deal with transphobes and then I saw the server icon and I'm like oh I'll be fine but surely there wouldn't be that many trans people here-

Apparently this is where all the trans people are

[hasty crown]

5 hours is very short, but its good youre enjoying

what are you learning?

[abstract kindle]

I'm kinda everywhere

A bit disjointed, I dropped out at a 10th grade level

I've been brushing up on division multiplication, negatives and positives, square roots and stuff like 5x+9=7 or 7(3x+5)=36

I've mastered all that now and the ai I'm learning from gave me something like (x-5)(x-6)(x+1)(x+4)=74

Which I've yet to crack because I'm challenging myself to figure out the formula myself rather than being told to formula

I'm sure for people in this chat something like that is light work though

It's been a very informal way of going about it

[hasty crown]

why are you using ai :p

theres plenty of online courses and books

[abstract kindle]

Because I'm a broke girl who can't afford actual tutors Dx and I learn well from the back and forth

[left scroll]

Hey all. When you get a cubic graph, it can be represented by a parabola. Now, when the parabola is decreasing is that the equivalent to concave down or f''(x)<0 for the cubic graph.

[oblique verge]

can anyone help me explaining to me how to derive the formula from a slice of a 3D geometrical figure from the x-axis? I am aware that I need a linear equation for that.

The geometrical figure is a cubed pyramid

$V = \frac{1}{3}a^2h$

[obsidian monolith]

Andy

[oblique verge]

Thank you.

[oblique verge]

what formula?

Do you mean the expression?

Just look up how to unwrap factored polynomials if so

[abstract kindle]

As said i am very new to mathmatics i dont know alot of the terms yet but ill def save this :3 tyty

[oblique verge]

What are you trying to do, again?

Find x?

[oblique verge]

Well, if the parabola is decreasing, the cubic's graph is concave down

[astral apex]

fyi, that last equation with the four separate x’s is probably too difficult for you to solve for now

if the number on the right hand side were 0 instead of 74, then it would be easy

but any other number than 0 makes it very unlikely to have any nice solutions

I just checked and the solutions aren’t something you can get by hand

[oblique verge]

[oblique verge]

ikr?

[indigo ruin]

yo guys im taking my pre calc final on tuesday :/ yall got any test taking tips 😭 my summer class didnt cover polars so ive been having a hard time on those (theyre on my final) and im so unbelievly bad at htrig functions and getting their equation given their grap

[vast onyx]

I just started too and AOPS Pre-algebra book is very good

then ill probably pick up the intro to algebra book and work up from there

[versed ledge]

generally with math just do problems, and make mistakes. figure out what went wrong, and improve from there

might already be obvious, sorry

[random widget]

Yeah I mean I can cope up with this since I have opted for add math although rule explanations and differentiation 1 is the same but I think questions are gonna be way harder so can u help me out?

[hybrid roost]

yeah of course, matrices and algebra go together if the matrices are representing linear functions

secondary education and university

but im confused why does college algebra exist

hear me out but people should skip from algebra 1 to precalculus just because precalculus is insanely algebra based

or no

algebra then geometry then precalculus

[willow skiff]

you're confusing me

which exams are you taking soon? is it the Add Maths exam you're taking this October/November?

[random widget]

Nah that’s 2027 m/j

But taking calc ab 2026 m/j

[mystic shuttle]

fr

[regal tree]

Gay is very math

[hot nest]

When im going through a text book, should I do all of the exercises?

[green haven]

Depends on the exercises, the book, and the complexity of the topic

If your book has 50 exercises on solving quadratic equations and you've already memorized the formula by the 30th, you can probably stop there

[hot nest]

Ah, I see

Sorry, just felt like there were a lot of exercises and that maybe I wasnt supposed to do all of them

[unreal monolith]

im new to this

[paper tartan]

@random widget @mystic shuttle @abstract kindle welcome to the mathcord c:

[paper tartan]

for topics in precalculus, authors usually lean on the side of more exercises rather than less

there's bound to be a lot of redundancy, and you certainly don't need to be able to solve every single last one in order to understand the subject

[random widget]

thx

[night violet]

prob the bestway

[abstract kindle]

Thank you :3

[shy night]

Very sorry for the long message, I hope this is an ok place to post this.

I didn't wanna take up a help channel from those that could make more use of it as I'm probably about to embarrass myself but this is probably one of the last few things I'm not quite grasping before my textbook throws me into calculus.

So a simple question of just... Simplify the expression cos(tan^1 x).

So I understand that it's asking "the cosine of the angle whose tangent is x". So I can replace the arctan x with y and have it as just cos y.

My textbook then tells me since we know tan y, it's easier to find sec y first. I assume this is because I'm also dealing with cosine and there's a Pythagorean relationship between secant and tangent. And that secant is the reciprocal of cosine. So far so good ... So when you solve for this, 1 + tan² y = 1 + x². I assume this value because tan y = x as implied earlier and since it's squared it's simply x². So sec² y = 1 + x². So then to get rid of the square on the secant I take the root of both sides.

Now with sec y = √1+x², I know that secant = 1/cos which reminds me that cosine = 1/sec. Well I have my secant value now and I'm solving for the cosine. So putting this back into the original expression it now becomes

Cos y = 1 / √1+x². What I'm failing to fully understand is if I do another method and decide that I want to make a triangle, I can only assume that √1+x² is the hypotenuse because it's adding two values together which looks like a² + b² = c². But how do I decide which leg of the triangle has the value or x or 1? That's the only part I think that I'm genuinely confused on.

Maybe I just answered my own question but I'll post this anyway for anyone else, but cosine says adjacent over hypotenuse to find the variable which implies which leg gets the x value so nvm... I think I get it now lol.

[modest bolt]

tan^-1 x = y
tan y = x
tan y = x/1
x→ Perpendicular/opposite side
1→ Base/Adjacent side

after you get these 2 sides, calc 3rd side with Pythagoras then find cos y

[shy night]

So the tan y = x already implies that x/1 which it's always y over x with that and that is what tells me which value goes to which leg? I think I get that too then, I'm just trying to be overly thorough and actually imagine it in my head before I move on. But simply remembering that would've helped me xD I often forget the simple stuff

[modest bolt]

what do u mean by 'its always y over x'? tan y = x, you can manipulate it anyway you want and convert it to p/q then by definition of tan, which is ratio of perpendicular and base, we take numerator as perpendicular and denominator as base and then form the triangle

you can take tan y = x²/x
perpendicular = x²
base = x
then, hypotenuse = √(x²+x⁴)

cos y = base/hypotenuse
= x/√(x²+x⁴)
= √[x²/(x²+x⁴)]
= 1/√(1+x²)

[hollow rune]

Tan Y = X means that X is perpendicular and 1 is base , so you can draw a triangle assuming Tan is in first quadrant then Hypotenuse will be √(1+X²) Now you can find each and every term like sec , cos , cot , cosec , sin .

[shy night]

I just haven't encountered the same terminology is all. But when graphing a slope it's always rise over run. I hadn't heard of the use of "base" before but it makes sense. Anyway, I do understand what I was trying to figure out in my own weird way I suppose. It was just something simple I should've remembered which typing about it helps me if I'm being honest to remember what I need to remember in the moment. But thank you guys anyway

[unreal monolith]

first time doing ts 😄

[slate heron]

Is that khan academy?

[unreal monolith]

Yes?

[trim salmon]

,w is 47^47 - 1 a prime ?

[obsidian monolith]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by sixscorpion4079_

[trim salmon]

,w is 47^47 - 2 a prime

[obsidian monolith]

Results provided by WolframAlpha

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Requested by sixscorpion4079_

[whole void]

,w is 47^47 - 4 a prime

[obsidian monolith]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by hockeydude85

[whole void]

,w is 47^47 - 6 a prime

[obsidian monolith]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by hockeydude85

[trim salmon]

,w is 47^47 - 48 a prime

[obsidian monolith]

Results provided by WolframAlpha

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Requested by sixscorpion4079_

[true geode]

@trim salmon @whole void I recommend not filling channels with nothing but bot commands - there's a separate channel, conveniently called #bots, for this

[trim salmon]

ok ty 🙂

[fast orbit]

hi im planning on skipping algebra 2, what are all the subjects i should know(ive taken geometry and am going to precalc)

[slate heron]

If you're skipping Algebra 2, I think you want to make sure you know how to solve and graph quadratics, work with polynomials and rational expressions, simplify exponents and radicals, and understand functions, their transformations, and inverses. You should also be comfortable with exponential and logarithmic functions, complex numbers, systems of equations, and basic sequences and series. As these are core skills learned for precalc.

[ivory igloo]

adding to this, you should review a lot of just number crunching, bc that comes in VERY useful in later math. 90% of the issue with people learning calculas is that they never learned algebra correctly

so basically i reccomend knowing linear equations etc. VERY well

and basic stuff that might seem obvious should be memorized :)

hope this helps

[ivory igloo]

(bc ur gonna forget it if its not memorized like 100%)

[restive gulch]

ummm.... i just started uni, what mathematics should i know since i have a short memory?

[faint sail]

What common fundamentals are always mentioned in every mathematical problem? I need to study the basics because I forgot about most of them...

[hushed sphinx]

At the high-school and initial university level, you can safely assume that all the math you were ever taught was because a good solid understanding of it is necessary for feeling comfortable and competent with the math that will appear at the coming levels. So if you want to read up, search your heart and mind for topics that make you think, "this never really clicked for me, even though I got lucky and managed to muddle through on the test/exam".
Exceptions to this include things with clear and obvious practical applications ("how does interest work"), as well as plane geometry with lines and circles and two-column proofs. (But coordinate-system geometry is important).

[hushed sphinx]

That goes for you too.

[mystic shuttle]

thanks

[rugged igloo]

is this a good breaking-down of the unit circle? i have shit memory so i made this to (hopefully) help

wait i got teh Q's wrong holup

there we go

dis better

[simple cedar]

Hi

I'm about to be g11 soon is pre-calculus hard?

[rugged igloo]

its the harder version of algebra 2 at my school bc they cover similar content, so if youve done algebra 2 it should be very easy and if youve done geometry and algebra 1 it shouldnt be too bad of a jump

also if ur talking abt ap precalc is seen as the esiest math ap

[simple cedar]

I'm still at g10 at first quarter

So far it's not that hard

[rugged igloo]

my firts day of 10th grade is today (its 2am) 😭

[simple cedar]

I was planning to advance study calculus though

[simple cedar]

Oh

[rugged igloo]

i took algebra in 7th geometry in 8th and precalc in 9th im abt to start calc in liek 7 hours (its the first class of the day 😭)

wait no like 6 hours

[simple cedar]

Wait what

You already have pre-calculus?

[rugged igloo]

ye

[simple cedar]

I though it will be taught in g11 stem or abm

[rugged igloo]

no it is just a math class that requires algebra and geometry to be taken,

what class are u taking this year?

[simple cedar]

Oh wait

I forgot

I'm from ph

So it's different

[rugged igloo]

philidel[hia?

[simple cedar]

I can't choose

[simple cedar]

Philippines

[rugged igloo]

o

[rugged igloo]

indicisive cant choose or not allowed to choose cant choose

[simple cedar]

We need to take all

[round hinge]

Hell naw💀

Sigma got that jawline😭

I have a question: it is normal that 17 years old boy is interested in math like these?

Idk, my friends are sayin that i should be interested more in football, girls, and other things

That i'm not a teacher or something

[regal tree]

im 17 too and love math

well almost 17

will be next month

[regal tree]

its not wrong to like different things lol

[round hinge]

Yeah, i shouldn't listen to opinions like this

It's just my hobby

[distant valve]

Wow…how close minded lol

You can be interested in whateveerrrr you want

[round hinge]

Yes

[distant valve]

Don’t let people pressure you into things you don’t like

[round hinge]

I agree

[distant valve]

I’m 14 and I’m also really interested in math (planning on studying math and or physics in college) and it’s kind of the same for me but instead of pressuring me into things I don’t like they kinda use me (copy off of me and cheat off of me even tho I don’t allow it)

[distant valve]

My classmates not my friends^

[round hinge]

Fr

[distant valve]

My friends are just as weird as me

[round hinge]

My real friend is Radim Szweda, he's good at philosophy and other stuff, but he has one problem, he can't understand math as me, so i help him, and he helps me

[distant valve]

Yeah that’s fine! :3 my friends also kind of struggle with math so I always help them, and in return they help me with stuff like social studies and history (I suck at them)

[round hinge]

Based

[lethal sparrow]

Has anyone here taken pre-calculous before

[noble lava]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you your question!
See https://dontasktoask.com/

[hearty quest]

trigonometry, logarithmic and exponential functions are precalc? wtf

[crystal idol]

wait thats exactly the same math classes i took in the exact same grades lmao

so im in precalc right now as a freshamn, but all my friends are in precaalc honors, and i dont wanna have a boring year, so I want to join them, but im concerned i wont get an a in the class. for reference, the teacher is giving extra credit everyday to help boost your grade because the tests are implied to be that hard. on the other hand, precalc would be really boring even if i might get an a. my past math grades in other highschool courses are a 99 in course 3, 99 in alg 1, and 98 in geo, and 96 in alg 2, so i waass wondering if i should take honors precalc. i am also trying to prepare for amc 10 while school is going on, so I was wondering what your thoughts are on this, whether i should go to honors or not

[crystal idol]

also im not lying abt my grades thats actually what they are

[nimble wolf]

Yes, I think you should.

[warped shuttle]

If the equation $|x^2 - 4|x|| = ax + 8/3$ have 6 roots what would be the range of a?

Can someone help with this ? I have graphed the left part of the equation and i know the line on the right should have a slope so it hits all of the points

[obsidian monolith]

GodOfPro

[modest bolt]

I think you have to find the local maxima and local minima(not including 0,0) of LHS and find the m for which the line touches the local maxima and minima and so you get your range of m.

[hushed sphinx]

From the graph, we see that when we increase a, the first time some of the roots disappear must be one of

1. the blue line loses contact with the parabola between x=0 and x=4. The equation for the relevant part of the parabola is 4x-x², so we can find the critical value of a by asking when the discriminant of 4x-x² = ax+8/3 becomes 0.
2. the blue line drops below the sharp corner at (-4,0). The slope where this happens is easily found by solving a·(-4)+8/3 = 0.
   By symmetry of the situation, the upper bound we find for a can then be negated to produce a lower bound.

It turns out that event (2) happens just at the value of a when the blue line goes through the local maximum of the curve at x=2 (but still has two distinct intersection points between 0 and 4), so it is possible to get the right answer using a flawed reasoning here!

[brisk dragon]

Does anybody know any good lectures or books that help with functions

[willow skiff]

James Stewart's Precalculus

[brisk dragon]

Aight thanks I’m doing Saxon advanced mathematics rn and this shit is so confusing

[willow skiff]

ohno, hope it becomes less confusing in future!

[carmine spruce]

in a basic context, the more you wanna learn, the more youll retain

good thing thats how math works

[rain flower]

guys can someone explain how this theorem works?

cause i can't understand how ( a^n > 1) cause a is already lower than 1 and also if we put in on fraction continues to be lower than 1

[hushed sphinx]

I don't think it actually works. It seems to claim that by knowing only that n<0 we can conclude (among other things) that 0<a<1, which doesn't seem to be likely.

[rain flower]

yeah

(how i do latex here)

i'll show the demonstration teacher used

[hushed sphinx]

Just put it in dollar signs or \[...\].

What they probably meant was that IF 0<a<1, THEN (a^n > 1 <=> n < 0).

[rain flower]

oh yes

let me see

[rain flower]

See if make any sense for you

it's supposed to be the demonstration or proof of it

[hushed sphinx]

That looks fair to me.

• A bit roundabout at first glance, but I think that's an attempt to make it maximally clear how "theorem 1" is being applied.
• A bit sloppy that the <=> and its right-hand side is omitted from the formula display after "we get:"

[rain flower]

ah sorry, let me show the theorem 1

[hushed sphinx]

I can imagine how it goes.

[hushed sphinx]

I don't suppose "e" actually means "implies" in your language, right? (I think it means "and" in Italian and possibly some other Romance langauges).

[rain flower]

means "and"

i forgot to translate lol

[warm hearth]

yo guys what are effectuve ways of finding range of a function without graphing it only algbra

[willow skiff]

what type of function? you can't do that without knowing the type of function

[warm hearth]

rational functions

ive found way by inversing but is there any better tricks

[willow skiff]

oh there's a technique for that!

I'm assuming you mean linear rational functions

so if you have y = (ax + b)/(cx + d), the horizontal asymptote is y = a/c, so the range is all real numbers except a/c

if you have y = h + a/(x - k), it's even easier cause the horizontal asymptote is y = h, so all real numbers except h

[warm hearth]

oo

[willow skiff]

yes and by inversing is how you show the horizontal asymptote is y = a/c

[warm hearth]

oh right makes it a bitr better now

[willow skiff]

I'll leave it to you as an exercise that the inverse of y = (ax + b)/(cx + d) is in fact, y = (dx - b)/(a - cx)

so the horizontal asymptote would be the vertical asymptote in the inverse function

what do we do to find the vertical asymptote?
dividing by 0 makes the expression undefined, so....

then yes a - cx = 0 implies x = a/c

[warm hearth]

okok another issue i faced wass

whern inversing smth which is quadratic u dont get a singlke x as subject

i found that i js use quadratic formula

but what to do when its hgher degree than 2

[willow skiff]

yeah, so there's two branches

the left part of f(x) becomes the bottom part of f^(-1) (x)

the right part of f(x) becomes the top part of f^(-1) (x)

[warm hearth]

okay

[willow skiff]

it's really, really hard to take the inverse

[warm hearth]

lmao

[willow skiff]

,w inverse of y = x^3 - x^2 + 1

[warm hearth]

cuz cubic and quartic formulas are insane and it was alreadu annoying to deal w the quadratic soo

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by sooouth.

[willow skiff]

exactly it gets exponentially more complex

also you should be aware that there is no general solution for the 5th degree polynomial and higher

it's impossible to create a formula for all polynomials

[warm hearth]

damn so what evn happens there do u js rely on computer algorithims then

[willow skiff]

yes

so you use numerical approximation methods

you can get as close as you want

like the issue is that we can't write the exact solution in terms of all the functions we know

we can keep inventing special functions for some cases, but that will never be enough in the general case

[willow skiff]

Newton's method, or Halley's method for example

[warm hearth]

oh ok

very cool

[upbeat nacelle]

someone can help, i dont know how to find F and i just tried to aproximate the function and tried to replace the values of the alternatives.
The G is a linear function and the F is a log function but i just cant realize how to solve for F

the problem asks for P coordinates

[calm harness]

Guys right functions is pre calculus

[willow skiff]

you can assume you have $F(x) = p \log_4 (x - h) + k$

[calm harness]

Alright👍

[willow skiff]

where p, h, k are unknown constants

[obsidian monolith]

south

[willow skiff]

so then the point (a, 0) must lie on the curve

$0 = p \log_4 (a - h) + k$

[obsidian monolith]

south

[upbeat nacelle]

oooh i see

so if i take (4, -2a)

[willow skiff]

hmm it's still quite messy, let me think

[upbeat nacelle]

but what is k

[willow skiff]

yeah I think the question assumes that h = 0

then it's solvable, two variables and two equations

[upbeat nacelle]

so its just plog_4 (a) + k

[willow skiff]

well, y = p log_4 (x) + k

https://www.desmos.com/calculator/msciza0r1k

[willow skiff]

yeah the question doesn't define which type of logarithmic function they want

[upbeat nacelle]

what i get that 4 = plog_4 (-2)

[willow skiff]

it's a broken question

[upbeat nacelle]

oh

[willow skiff]

if you receive the solution

there's going to be some hidden assumption in there

[upbeat nacelle]

yea i will ask to my teacher beacuse he have the solution, i spend a lot trying to realize how to solve it

[willow skiff]

no worries! seems like only your teacher knows

[upbeat nacelle]

yea anyway thanks for helping!

[viscid thistle]

dog??

[upbeat nacelle]

yea its my dog

[viscid thistle]

:/

[viscid thistle]

By the way guys

I have a hard time to understand this math problem

[tacit pawn]

is that chihuahua

[viscid thistle]

What is growing exponentially mean?

[tacit pawn]

growing exponentially means that its graph would look like an exponential graph basically

like a parabola

[viscid thistle]

So if an algae growing exponentially and it is doubled in a day, how do we write the function?

???

[tacit pawn]

function would be of the form y=x^2

x= days and y=size

actually it should y=(x^2)A where A= original size of algae

[hushed sphinx]

No.

Exponential growth would be y=2^x, not y=x^2.

[tacit pawn]

oh yeah my bad

2^x

y=A(2^x)
A=original size of algae
y=size
x=days

but i think it should be (x-1) as the exponent cuz on day 1 it would be the original size

which mean 2^0

am i right?

[hushed sphinx]

Just call the first day "day 0".

[tacit pawn]

yeah that can also be done

[hushed sphinx]

That's how many days have gone past since the beginning, after all.

[tacit pawn]

yeah

[upbeat nacelle]

yea

[tacit pawn]

nice

[faint sail]

Hello!!!

May I ask how to solve for time?

[tacit pawn]

?

[faint sail]

Like seconds

Wait, I'll just show picture...

What steps should I make to get the answer? It's definitely not addition

😢

[soft plover]

Hint: LCM

[hushed sphinx]

I think we first need to figure out what was meant by "stops at every 56 seconds".
Perhaps it's a typo for "stops at some floor every 56 seconds" -- but then we wouldn't have enough information to know anything about when the two elevators stop at the same floor together.
Or perhaps it means "stops at the ground floor every 56 seconds" -- but then it's either an extremely fast elevator, or a rather short skyscraper.

[faint sail]

This is exactly my problem

[faint sail]

I found the answerrr it's 168 seconds

Thankieee

[hushed sphinx]

Realistically, you're probably expected to calculate lcm(56,84) -- but it's a horribly phrased problem that doesn't really in itself make that solution sensible.

[faint sail]

Probably why I was confused

Thank you!!!

[hushed sphinx]

Alternatively:
Suppose the "skyscraper" has 11 floors (numbered G, 1, 2, 3, ..., 10), so a round-trip for an elevator means moving one floor 20 times.
Elevator 1 moves by one floor in 2.8 seconds; elevator 2 moves by one floor in 4.2 seconds.
Then after exactly 33.6 seconds the fast elevator has been to floor 10 and opens its door at floor 8 on the way down. At the very same time the slow elevator reaches floor 8 on the way up. So this is the first time when they "stop at the same floor together".
So in that case the answer is (5) none of the above.
But it only works if the number of floors is one more than a multiple of 5.

[storm shuttle]

why does it look incomplete 😭

oh wai

so it stops but for 0s

🫠

oh nvm

it stops