precalculus

[viscid thistle]

I am modeling the population growth of the Netherlands, and what can I use to fit data into logistic and exponential growth models?

[sinful halo]

you can rewrite this as $2(\frac{ln(x)}{ln(2)})=x$

[obsidian monolith]

prime

[sinful halo]

ah, this is an intermediate step

[exotic skiff]

Can anyone please guide me;-;

[arctic dragon]

Can you explain how you got this please

[willow skiff]

dude this is the precalculus channel

you want to go to the calc channel

[worn cape]

I can help you in dms if you need

[charred fiber]

I got a question. I had to determine if a equation would be even and odd on a graph by using f(-x) and -f(x) on a quiz. I got the answers right; however, she subtracted 1 point off of each question because when showing my work I didn't include f(-x) and -f(x) in my problem. So for example I wrote 2x+4 instead of f(-x) = 2x+4. She never told the class this. The answer she wanted was either odd or even so I just did the work and didn't bother labeling because I only needed to circle odd, even, or neither. But those points she subtracted off left me with a 19/22 on a test that I would have gotten a 100% on. Is this fair? Should I ask her about it or is it my fault?

[jovial seal]

To be honest, it seems more like miscommunication than a fault on your part, so you could talk about it to your teacher. Tell her you understood the concept and correctly identified whether the equation was odd or even, even though you didn't write out f (-x) and -f (x), and that the main understanding was the mathematical concept, and the labeling requirement wasn't explicitly communicated.

[charred fiber]

okay thanks 👍

my friends who got a 100% on the quiz said that they just put that there out of habit and also didn't know you had to as well. And they all said I should talk to her about it.

[viscid thistle]

What are some great books that teach precalculus through real world applications like physics or engineering?

[normal coral]

everyone always sees the precalc channel and is like yep, precalc has integrals

[remote mesa]

its cause they take the 'calc' in precalc too far

[warm oyster]

then arent we allowed to ask help for integrals etc things here?

[willow skiff]

not in this channel

you should ask in #calculus

[warm oyster]

but the channel belongs in early university

so im confused

[shadow summit]

are you learning this stuff in high school, and if so, are you perhaps doing a higher math class?

[warm oyster]

calculus is a part of high school wdym

derivatives, limits belongs to this channel right?, arent they

[untold shuttle]

PRE calculus, thus stuff you learn BEFORE taking calculus

[hushed sphinx]

In the US, whose traditions inform the channel organization, calculus is commonly taught in the first year of university. Therefore the #calculus channel is located in the "early university" category. That doesn't mean one has to actually BE in university to use it. The categories are just a practical arrangement to avoid having all of the channels lumped together in one long list.

[warm oyster]

oh ok, thanks 👍🏼

[untold shuttle]

wait calc is for university?

????????

i never knew that

interesting

[hushed sphinx]

Depends on which country/system you're in.

[elfin matrix]

this

calc can be taught at pretty much any level depending on the country and education system

[elfin matrix]

typically, unless youre taking math as a course, most university STEM courses etc will require you to do math as a module which includes calculus

[hushed sphinx]

I'm led to believe it is not all that uncommon in the US to learn calculus in high school. They just tend to think of it as "particularly bright/interested students get to learn some university topics early".

Conversely, it is not uncommon to see basic calculus taught at European universities -- just billed as "remedial high-school mathematics for STEM students who followed a low-math track in high school".

So the actual differences on the ground might not be as profound as the overall generalizations suggest.

[untold shuttle]

im a hong konger taking IB. Usually we math nerds get taught it early in 10th or 11th, but we also have it for 9th grade as a super-extension task. I am a freshman, but because of 🤓 , i've already learnt the equivalent of roughly 25-30% of calc 1

including me, there are 3 people in my maths class (higher level, rigour based, we call it "Pure maths") who know calc

i thought it was a high schooler subject

[deep prism]

hi

help

[vagrant goblet]

hi whats the log in base 1 of 1?

[hushed sphinx]

"Log in base 1" does't make sense.

[thin roost]

can anybody explain the rational root theorem and how syntetic/long divison for polynomials work

like why does the algorithm work

[wet nest]

Can anyone help me to solve this?

[wet nest]

Eq. 41

[viscid thistle]

dawg is this multi variable calculus

[twilit eagle]

nah precalculus 💯

[viscid thistle]

watch youtube videos about the topic; just search up on youtube about the rational root theorem and long division...and you will understand my friend

[valid parrot]

Is there any limit
[ \lim_{x \to k} f,(x) = 0 :, \quad \lim_{x \to k} g,(x) = 0 :, ]
such that
[ \lim_{x \to k} {f,(x)}^{g,(x)} \neq 1]

[obsidian monolith]

ταυταυ

[valid parrot]

I found one btw

[thin roost]

ive been finding videos on its application

i havent been able to find any videos on the why though

ill keep searching

[grave bear]

anyone know why ap precalc is a thing now

[smoky pendant]

for these problems do you reflect first, translate left/right, then up/down?

for example, 37 would be reflect over x axis, then shift 1 right, and up 2

[whole spruce]

quick question is ratio of cotθ the same thing as finding the exact value?

[viscid thistle]

u by ratio u mean the ratio of the lengths of the triangle sides

then yeah

[whole spruce]

im sorry to bother, but can you help me with this question? given sinθ = 4/5, secθ<0, determined the ratio of cotθ

[whole spruce]

inverse of tangent

1/tan?

Not sure

[worn cape]

and how can you rewrite tangent then?

[whole spruce]

idk what youre trying to ask, i just know that cot is inverse of tan

[worn cape]

There’s a special way you can rewrite tangent in terms of sine and cosine

and since cotangent is the reciprocal you can flip that

[whole spruce]

I tried the question myself, is the answer cot = 3/4?

[viscid thistle]

draw out your triangle it makes things easier

[whole spruce]

I understand that

[viscid thistle]

yes

now why do you wanna confuse the lad

bruh

ok

[worn cape]

Wait so how did you solve it?

Can you put your work in here?

[whole spruce]

I could

[viscid thistle]

derive what

that tan=sin/cos?

[worn cape]

will you though

[viscid thistle]

oh

ok

[whole spruce]

that’s basically what i did

[viscid thistle]

what

ig?

that works

[worn cape]

yeah that’s a valid way to do it

[whole spruce]

am I complicating myself?

[viscid thistle]

not that ur way is complicated but there's an easier way

[whole spruce]

Is there an easier way ?

[worn cape]

but the way we were thinking is by doing cot (theta) is cos/sin

then you sub in the value for sine and the pythagorean identity version of cosine

and plug in and simplify

your way is completely valid and probably less abstract anyways

[whole spruce]

If one of you guys can write it down for me, that’d be great

[viscid thistle]

u don't even have to use that you can just use sohcahtoa

[worn cape]

you still have to solve for c that way, it’s basically the same

[viscid thistle]

u can understand the sin bit through sohcahtoa

[whole spruce]

secθ<0
can someone explain this to me?
i view it as when cosine is + or is it -?

The inverse

The negative

Sec=- ?

[slim steppe]

It's not the inverse

It's the reciprocal of cosine

[whole spruce]

oh

not sure

[slim steppe]

I just told you

😦

1/5

or .2

[whole spruce]

1/cos

This sign means “<“ greater then right?

So then cosine is greater then 0?

its the same question from above

i just want to make sure I understand it

Cause i guess on that sec part

all i want to know is
when sec < 0 is equal to +
when sec > 0 is equal to -
?

when putting it inside the quadrant

ok thanks

I havent learn that yet, but it’d come in handy soon. I appreciate the help

[dry chasm]

While finding max of function using derivative can we directly assume the point of Max the point we get after equating first derivative to 0 without checking the sign of second derivative ?

[raw hill]

no

Consider x^2

[viscid thistle]

Isn't it suppose to be 6x¹ not 9x² ??

[warped plume]

no

its simplified, not chain rule

[viscid thistle]

Then he just calculated the 3² so it became 9x² ?

[dry chasm]

Oh okay thanks !

[slim steppe]

Well, I believe the correct way of saying it would be "the negative reciprocal"

[warped plume]

its the quantity squared, so yeah

[cinder prairie]

hi calculus here 😎

[warm oyster]

damn

[wind flint]

C A L C L U S

calclus is best type of calculus

fr

[cinder prairie]

ikr?

[steady bear]

Yo calculus can you tell your friend statistics that nobody likes him and he should just leave this plane of existence

[warm oyster]

[cinder prairie]

Will do

[steady bear]

Lmfao

[warm oyster]

predicting

[slim steppe]

bravo to the people that have actually went into that field of research

[summer mirage]

Quick question: How do I verify this identity?

sinx/cosx (I just simplified if from tanx)

[summer ruin]

do something about left hand side

[snow root]

Hold on am I bugging or does the left simplify to -cosx

If u plug in pythagorean identity for 1

[summer mirage]

I did

The original identity was:

[summer mirage]

This is the original identity.

[summer ruin]

what is your question?

why is there a second identity and which one are you asking about

[snow root]

How did u go from this to the first pic

[summer mirage]

nvm,

It is solved]

Someone just explained it to me

Thanks tho

[snow root]

Can u send solution I am curious

[summer mirage]

yeah

hol up one sex

sec*

NOT THE OTHER WORD

sec*

[snow root]

Lol

[summer mirage]

Original:

Result

[snow root]

Hmm

1+sinx-cos^2x becomes sin(1+ sinx)

Ok that makes sense

Thanks

[summer mirage]

you're welcome

[summer mirage]

Do I cancel out the 9/4 sec^2theta. Or do I simplify the radicand first?

[summer ruin]

there's nothing to cancel

[white lion]

oh lord

[summer mirage]

I did

Thanks tho'

Much appreciated.

[solar olive]

-1 + sin(x)^2 = -(1 - sin(x)^2) = -cos(x)^2
-cos(x)^2/cos(x) = -cos(x)

[viscid thistle]

Why the answer here is -√3 not √3 ??

[uncut mulch]

you dropped the - sign from the previous line

which came from chain rule/derivative of
35 - 5sec(x)

also with the presence of differentiation, it's calc not pre-calc
please use the correct topic or claim your own channel

[viscid thistle]

you're missing a U 🤨

[cinder prairie]

No way 🤯

[viscid thistle]

Thank you ❤️

[shadow summit]

You can’t cancel the $\frac{9}{4}\sec^{2}(\theta)$, you can rationalise the denominator though, but that would make it very chunky. It depends on what is expected of you to do, but I probably wouldn’t change anything about this.

[obsidian monolith]

TheLord26

[north sable]

Is there a section for calculus bc I am taking AP calculus ab

[crimson prism]

uts probably grouped together

[terse tiger]

How you taking geometry and calc

[crimson prism]

ryan has been exposed

[vast quartz]

just #calculus 😭

[cinder prairie]

dont tag

[whole spruce]

when its csc(5pi/2) can i look at it as sin(5pi/2) ?

[hushed sphinx]

Both csc(5pi/2) and sin(5pi/2) happen to be 1, so they are the same -- but only for that mostly accidental reason.

[whole spruce]

how to i go from exact values to radians
example -> cos(1/2)
what would that be in radian form?

[hushed sphinx]

Huh. Do you mean the cosine of half a degree, and you want to write that half a degree in radian form?

[whole spruce]

i figure it out,
cos (1/2) = pi/3, 5pi/3
thats all i wanted to know

[hushed sphinx]

Huh?

Did you mean arccos(1/2)?

[whole spruce]

maybe i wasnt clear with my question

my question says costheta=1/2

[vapid plaza]

You mean to say the solutions to cos (x) = 1/2 are x = pi/3, 5pi/3.

[open plank]

trigonometry is fun !

[restive carbon]

Hello I need a little help with precal

How do you find the slope on a graph ?

[glossy delta]

At any given point or like finding secant lines

Given 2 points

[glossy delta]

If it's linear like a line you can just do rise over run

Difference in y/difference in x

[dusty bear]

can anyone teach me calculus

since, idk anything

[glossy delta]

What about calculus

[dusty bear]

.

tell me where i can stuy caluclus ( 0 money )

@visual trail

[glossy delta]

In your highschool probably

[dusty bear]

bruh

i in (

im in 9 th grade but i wanna learn calculus

[gaunt carbon]

probably youtube or something
you might wanna work on algebra and trig some more before you start studying calculus though

can't really do it well without the foundational stuff

[glossy delta]

^

Calculus is 99% algebra

[gaunt carbon]

literally tbh

[dusty bear]

ik trignometry and algebra

trignometry basic lvl

lol

[gaunt carbon]

have you done like. csc sec and cot stuff

[dusty bear]

yes

i k the basic identites

what grade are u in ?

[gaunt carbon]

I'm in 11th grade

[dusty bear]

W

[gaunt carbon]

when it comes to algebra how do you feel to that end

[dusty bear]

ik these many identites

not the below let part

[dusty bear]

personally i likee algebra more than anything in maths

[gaunt carbon]

okay cool

if I were you instead of looking at calculus i'd become more familiar with trigonometry
probably look at trigonometric equations, polar coordinates, and complex numbers just to get again a good base
they usually come in handy later
and then when it comes to algebra if you haven't done this stuff already I recommend getting very very comfortable with conic sections and piecewise functions along with inequalities
all those are really prep for calculus
if you want to dive straight in though, I would check out 3blue1brown's video on the subject and maybe see if you could do some on khan academy as they have fairly in-depth calculus resources

[dusty bear]

i have basic idea on complex nos

but thnx i really aapreciate

[gaunt carbon]

yeah of course

[dusty bear]

which country are u ?

[gaunt carbon]

from the US

[dusty bear]

oh ok

[shadow summit]

calc on top, linear algebra scares me

[valid parrot]

linear algebra in uni is very fun you'll see

[shadow summit]

i do uni-level linear algebra, its definitely not fun.

[valid parrot]

yeah

xdd

[gaunt carbon]

linear algebra truly is iconic tbh

[valid parrot]

i love it

[crimson prism]

uhh js go on yt or start with the stewarts textbook

if u wanna learn p basic calc go up till chp ig 6?

after that its haevy integratation based

also make sure u can do basic math rly well cuz like it is very heavy algebra based when ur solving the stuff

imo u dont rly need precalc for calc

[gaunt carbon]

you dont need it necessarily but it does have its usefullness later down the line

[plain frigate]

Guys,would you mind some of you can help about that

[hoary meadow]

Solved in #prealg-and-algebra

[willow skiff]

thanks for the heads up btw

[warm spoke]

2 + 2 is 4 minus 1 is 3

[inner moat]

can someone help with composite functions

[brisk adder]

Those are not composite functions

Can you show what you have so far?

[hushed sphinx]

They're plainly composed of f and g (and the addition and subtraction operations).

[halcyon trout]

Anyone can help me with this

[heady elbow]

help

[halcyon trout]

1. ( \lim _{n \rightarrow \infty}\left(\frac{2 n^{-2}(n !)^{3}}{3(n-1) ! \cdot(n+1) ! \cdot(n-2) !}\right) = \lim _{n \rightarrow \infty}\left(\frac{2 n^{3}}{3(n+1)(n-2)}\right) = 0 )

2. ( \lim _{n \rightarrow \infty}\left[2 n^{2}\left(\sqrt[3]{2 n^{3}-1}-\sqrt[2]{2 n^{3}+1}\right)\right] = \lim _{n \rightarrow \infty}\left[2 n^{2}\left((2n^3)^{1/3}-(2n^3)^{1/2}\right)\right] = -\infty )

3. ( \lim _{n \rightarrow \infty}\left(\sqrt{n^{2}+5 n+3}+\sqrt{4 n^{2}+2 n-1}-3 n\right) = \lim _{n \rightarrow \infty}\left(n\sqrt{1+\frac{5}{n}+\frac{3}{n^2}}+2n\sqrt{1+\frac{1}{2n}-\frac{1}{4n^2}}-3 n\right) = n )

4. ( \lim _{n \rightarrow \infty} \frac{\sqrt{n+2}-\sqrt{n-1}}{\sqrt{9 n^{2}+2}-3 n} = \lim _{n \rightarrow \infty} \frac{1}{3\sqrt{n}} = 0 )

5. ( \lim _{n \rightarrow \infty}\left(\frac{1+3+\ldots+(2 n-1)}{n+3}-n\right) = \lim _{n \rightarrow \infty}\left(\frac{n^2}{n+3}-n\right) = \lim _{n \rightarrow \infty}\left(\frac{n(n-3)}{n+3}\right) = \infty )

6. ( \lim _{n \rightarrow \infty} \frac{1+\frac{1}{2}+\frac{1}{3^{2}}+\ldots+\frac{1}{3^{n-1}}}{1+\frac{1}{5}+\frac{1}{5^{2}}+\ldots+\frac{1}{5^{n-1}}} = \frac{\frac{3}{2}}{\frac{5}{4}} = \frac{6}{5} )

7. ( \lim _{n \rightarrow \infty} \frac{\sqrt{n}}{\sqrt{n+\sqrt{n+\sqrt{n}}}} = \lim _{n \rightarrow \infty} \frac{1}{\sqrt{1+\frac{1}{\sqrt{n}}}} = 1 )

8. ( \lim _{n \rightarrow \infty} \frac{n \cdot \sin n}{n^{2}+1} = 0 )

9. ( \lim _{n \rightarrow \infty}\left(\frac{\mathbf{1}}{\mathbf{1} \cdot 3}+\frac{\mathbf{1}}{2 \cdot 4}+\ldots+\frac{\mathbf{1}}{n \cdot(n+2)}\right) = \frac{1}{2} )

10. ( \lim _{n \rightarrow \infty}\left[\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right) \ldots\left(1-\frac{1}{(n+1)^{2}}\right)\right] = \frac{2}{3} )

[obsidian monolith]

Zeuro

[halcyon trout]

@heady elbow check

[arctic magnet]

Holy

[halcyon trout]

Can anybody help me with this

[tropic bone]

Is it asking for the rate per hour?

[plain frigate]

Folks in this graph problems ,we suppose to use vertical and horizontal asymptote or Someone have a idea ?

[granite temple]

103?

[granite temple]

so 340 = 170(1+x)^5 where x is your percent

[plain frigate]

Yes this one

[gaunt carbon]

basically you're able to tell graphs based on their shape and where the holes are
the holes being where things on the top and bottom camcel

[whole spruce]

for this equation can you cube a negative number?

[hushed sphinx]

Why wouldn't you be able to?

[whole spruce]

so you can cube a negative number?

[gaunt carbon]

yeah?

[whole spruce]

so when i cube it does it become -1? like how you would square root 1?

[tender mist]

I think I see what you're asking. Yeah, it's possible to do that. All odd roots are able to be done on positive or negative numbers. It's only even roots that are bound to positive numbers

[whole spruce]

when i cube it, it becomes 2cosx=-1?

[hushed sphinx]

Umm, what is the "it" you're cubing to get that?

[whole spruce]

the equation up there

[whole spruce]

that^

[hushed sphinx]

Cubing (each side of) that gives 512cos^9(theta) = -1.

[whole spruce]

im isolating the equation to find cosine

[tender mist]

You isolate by doing the opposite operation. So dividing by 8, and cube rooting

Which is why I mentioned the odd and even root thing. Thankfully since it is an odd root, you can root a negative

[warm spoke]

@exotic barn ok so i noticed that when you have a zero in the denominator thats not in the numerator of a rational function thats a vertical asymptote and if theres a shared zero in the numerator and denominator then its a hole but is it possible to have a jump

[exotic barn]

yeah, why did you ping me hahaha, you said the same thing previously to that girl of yours lol

[warm spoke]

on god shes my girl 🥶 but i pinged you because you r smart

[exotic barn]

haha thanks

[warm spoke]

i cant think of when a rational function would have a jump

im getting the vibes

that it has something to do

with limits

and rates of change

but vibes only take you so far

[hushed sphinx]

Rational functions don't jump, but they can have vertical asymptotes even where the numerator is 0 -- consider for example x/x².

(Silly example, but the instances of this are generally silly in the same way).

[warm spoke]

mannnn

why cant they jump though

oh wait

rational functions are just polynomials

nevermind

i mean any function with a numerator and denominator part

[hushed sphinx]

Hmm, I don't have an elementary argument for that ready.

[warm spoke]

nah ur good i kinda get why polynomials dont jump but if u got an explanation at any point pls share

[hushed sphinx]

Well, in that case |x| / x does jump.

[warm spoke]

how would you identify jumps in a graph

other than by just looking at it

[hushed sphinx]

I'm not sure how to do anything with a graph that's not looking at it ...

[warm spoke]

moreover how would you describe them like would you describe them by their left and right point and which point is defined

[warm spoke]

noo i mean like

actually

idk what i mean

[dusky current]

If f(x) = x^3-5x^2-4x
and g(x) = 2f(x) + q
Find all values of q if g(x) has exactly one x-intercept

[half vector]

hello guys, u discuss here about the basics of calculus?

[stable vessel]

Can someone help me

What this notation means?

[warm oyster]

closed interval

[stable vessel]

So it is the union of -infinite to -3 and 0 to infinite?

[warm oyster]

are you talking about the red one or the blue one?

[stable vessel]

The red one

[warm oyster]

oh okay so yea it is the union of -infinite to -3(not included) and 0(included) to + infinite

and the x in blue is thier final result, that is thier intersection

[stable vessel]

This is another part I don't understand. Every negative x ≤ -3 would result on the equation "x²+3x" being ≥ 0

Why it shortened it to [0, 3]?

[oblique sapphire]

you mean $\cup$ and $\cap$ right

[obsidian monolith]

RottenGold

[oblique sapphire]

$\cup$ is called the "union" of 2 sets, it combines 2 set. $\cap$ is the "intersection" of 2 sets, it finds the overlapping elements of 2 sets

[obsidian monolith]

RottenGold

[stable vessel]

Oh, I understand now

I missread the question

[warm oyster]

lmao that happens

[stable vessel]

Because of |x| ≤ 3

A thing I hate about learning maths is sometimes having to spend more than half an hour on a single page tl understand it, but it is fun

[unique path]

you can take the cubic root out of the equation, it would be 2cosx=-1 then cosx=-1/2 and finally arccosx=-1/2 then x= 120 or 2pi/3

[lunar cairn]

hello everyone i have a question , im 10 grade right now and i want to start learning precalc and after calculus by my self but i dont know where can i start can any one tell me the roadmap or something like that

[viscid thistle]

I recommend using An igsce addmath book

That's where I studied all my base of calculus from

[lunar cairn]

alright thanks let me search about it

[digital mirage]

is this not a dirichlet function ?

[vast quartz]

I'm studying my precalc with the openstax book

[viscid thistle]

Ill tell you chapters that are normally hard is binomial and vectors

The calculus part such as derivitives and intergrals are easy

Trignometry is also a hard chapter

[lunar cairn]

so which one i have to start first and also i want to take ap calc ab at next year

[viscid thistle]

The book starts of with functions

I sent you in dms

The book I used

[lunar cairn]

ok i got it

thanks

[viscid thistle]

Just follow that

That was my grade 9 and 10 book

[tender mist]

Just curious what I should be finding with a question like this. I understand the end goal, and generally what it is I'm supposed to do, but I don't really know how to start it

I'm just self-learning, and I'm not in an official course, so I'm just a bit confused. My school back then never really covered trig with functions, so I'm inexperienced with this type of situation

I don't need the answer, just want to know what processes I should be applying to that question

[gentle kettle]

so just xor?

symmetric difference

[strong epoch]

Does anyone know how to simplify this

[warm oyster]

idk think it can be simplified any further but the only thing i can make sense of is multiplying both side by 1-sin theta

@strong epoch

[strong epoch]

I tried that

Got that bottom would become cos^2x

Then wouldn’t it be -cossin/cos

I thought it was -sinx but it was marked wrong

[uncut mulch]

how are you getting
-cos(x)sin(x)/cos(x)

[strong epoch]

Doesnt cos/cos^2 simplify to 1/cos

[strong epoch]

What would it be the

N

[uncut mulch]

cos/cos^2 does simplify to 1/cos,
but you don't just have cos/cos^2

[strong epoch]

I know that’s where the -cosxsinx comes from

Can I just simplify it like that?

[uncut mulch]

no

[strong epoch]

Oh

Why

[uncut mulch]

fractions get simplified from cancellation of a common factor
and not erasure of expressions that happen to appear

[strong epoch]

Oh yea

So I can’t do that

Fruck

I don’t know how I would simplify it further

[uncut mulch]

here you'd want to factorise the numerator
or not have expanded in the first place

[strong epoch]

So -cos(sin)

[uncut mulch]

no

[strong epoch]

1-

?

[uncut mulch]

no

[strong epoch]

What is it cos( 1-sin)

[uncut mulch]

yeh

that'd be the unexpanded numerator

[strong epoch]

Cos( 1-sin)/cos^2x

[uncut mulch]

$\frac{\cos(x)(1-\sin(x))}{\cos^2(x)}$

[obsidian monolith]

ℝαμΩℕωⅤ

[uncut mulch]

now that it's clear that cos(x) is a factor of both the numerator and denominator, you can cancel

[strong epoch]

1-sin/cos

Thanks

[fast plover]

not really sure how to finish this question

this is my working out, but i dont know how to eliminate the value for a

[fringe quest]

Just use the formula sin-1 x + sin-1 y

Then we know that sin-1x = pi/2-cos-1x

Then just euqate the angles for x

[willow skiff]

alternatively, take the sin/cosine of both sides

the identities can be found from a right triangle

[shadow creek]

anyone have any tips for gauss elimination

[spark moat]

google fang cheng

its gaussian eliminqtion without fractions

https://youtu.be/Nuoq-qdLrmo?si=0xhChLwZwMblUY_b

and then convert to gauss-jordan

https://youtu.be/P4VTYmbyxOg?si=Iuz07V_RmVnxF9z4

[shadow creek]

ik how to do it

i just want tips

on what should i start with and what not

[spark moat]

this is seperate from gaussian elimination

well its a type of gaussian elimination j without fractions

[shadow creek]

it's standard gaus

[spark moat]

no bc this way avoids fractions

[grave crag]

Can anyone explain how to solve this problem? I posted the solution as well.

[whole spruce]

How do i find this point? Where the arrow is pointing
im looking for the phase shift of the function

[summer ruin]

solve f(x) = 0

[potent gull]

I urgently need someone who knows Calculus

[frigid trout]

Google is pretty good at it

[shadow summit]

if you know the function of the graph, you can find the phase shift. in the form $a\cdot\sin(b(x+c))+d$, a is amplitude, b is the period, \emph{c} is phase shift and d is verticle shift. in the form $a\cdot\sin(bx+c)+d$, the phase shift is found with $\frac{c}{b}$

[obsidian monolith]

TheLord26

[open badger]

what is

2cm+4cm(4+1)

[willow skiff]

it's 2 cm + 4 * (4 + 1) cm

[shadow summit]

22cm

[whole spruce]

im suppose to write an equation for the graph, ik the amplitude, and vertical displacement, im missing phase shift and period

[shadow summit]

Just approximate then, you aren’t given any exact values.

[whole spruce]

the only values im given is the numbers that are marked on the graph

[shadow summit]

If that is all the information you have got, then this is the answer: $y=6\cos\left(\frac{2\pi}{3}\left(x+\frac{\pi}{24}\right)\right)-2$.

[obsidian monolith]

TheLord26

[shadow summit]

What with?

[fervent crag]

What do I need to know before I venture into calculus?

[whole spruce]

is there an equation i can use to find the phase shift or period?

[shadow summit]

Count.

Basically what I did was counted how big each of those units are, which was pi/24, from there it was pretty easy.

[worn cove]

trig

and a good amount of algebra

[shadow summit]

Algebra

Calculus is 90% algebra

[worn cove]

yeahh

i gotta step up my algebra game more ngl

im not in college still but next semester, i'll be taking up basic calculus

[shadow summit]

The most important things that you should revise is logarithms, exponents, fractions. (At least that’s what I think)

Also if you’ve done complex numbers before those are pretty annoying to divide.

[arctic sundial]

Help

I don’t understand why it’s not the thing I circled on the top (not the answer)

Isn’t converting it to a different time rate make it like that?

[shadow summit]

Because the value increase one per month, it stands to reason that it will increase 12 times per year. And because t is time in years, you have to multiply the value by 12.

What you have done is multiplied 12 (the number of times the price increase per year) by t/12, which cancel out, thus leaving you with just t.

And because the price doesn’t increase only once per year this is wrong.

[arctic sundial]

Omg Ty so much

[fervent crag]

Okay I can do most algebra

Trig needs more work

[tender mist]

For a bit of background context, I'm technically not in school right now, and haven't been for a little while, so while I have taken pre-calculus before, I'm a bit rusty. I understand what the question is asking me to do, but I'm not sure how I'm supposed to go about doing it. Can anyone tell me what formulas or rules I'm supposed to use on this one? Not necessarily asking for the answer (you can provide if you want, I don't mind), I'm just curious about the process itself

[elder bane]

Help, what are the rules for integrals

[warped cipher]

,tex .int rules

[obsidian monolith]

Akira (fumo)

[warped cipher]

usually integrals belongs in #calculus

[left zodiac]

i was doing random stuff with exponents when i found smth weird
so i have x^x right, and it's defined on [0;+infinity[ since apparently 0^0 is 1
but as far as i know you can write x^x as exp(xln(x)) which cannot be defined on 0
my question is where did i go wrong, is there something i didn't do correctly when i rewrote x^x ?

[summer ruin]

because 0^0 is not 1, it's undefined

[tender mist]

What about this? I've been having trouble with this, lol

[left zodiac]

ah, i've seen from some sources that it's 1

thanks

[summer ruin]

draw the picture

[shadow summit]

Pro tip for math: don’t mess with 0.

[left zodiac]

i guess i'm just gonna

[gentle sapphire]

Guys, what algebra and trigonometry do i need specifically to be able to understand calculus?

[shadow summit]

👍

[summer ruin]

all of it

[left zodiac]

a whole lot of algebra

idk about trigonometry

but probably all of it too

[shadow summit]

Lol I thought that as well when I first read the message.

[gentle sapphire]

all of the algebra and trigonometry? wdym by that? Everything that has been published? 😄

[shadow summit]

Google “what does a pre calculus course have”

[summer ruin]

everything that's part of the school algebra and trig course

[shadow summit]

Ahh yes, my favourite precalculus course, Algebra A.

Once again, calculus is 90% algebra

[tender mist]

I generally know what it looks like, the problem is I'm not sure about the equations. I don't think I'm supposed to find the answer with a graphical solution

[summer ruin]

it's not like the exercise explicitly forbids you to use valid mathematical tools?

[tender mist]

Of course, but I'm pretty sure there's an algebraic solution, no?

[summer ruin]

once you draw the picture the equations will be obvious

I mean if you can't even visualize the problem in your head and what it's asking, then it's not clear how you would come up with algebraic solution

[kind topaz]

taylor series

[tender mist]

I wouldn't have a problem with the question if it was asking for just a function period. But it's asking about the function of the slope. I'm not sure how to create the final answer based off of just that variable

[summer ruin]

try to figure out the slope of the line joining P with the origin first

[tender mist]

And is a graph required to do that? Like I can't do it any other way?

[summer ruin]

depends on how well you understand what the problem is asking

you already given the information what the coordinates of P are technically

in the problem statement

[tender mist]

The problem is, I don't know how to find the coordinates. I was trying to find them earlier, but I must've been doing it wrong. That's why my original question was asking what equations or rules I have to use to find it. I've done a problem like this before, but it was years ago, and I'm just rusty

[summer ruin]

suppose P has coordinates (p_1, p_2) and you're given that P lies on the graph of f(x) = sqrt(x)

what can you say about coordinates of P now?

and it being in the first quadrant

[shadow summit]

Try graphing stuff on Desmos.

[tender mist]

Am I just misunderstanding the question?

[shadow summit]

What do you think the question is asking?

[tender mist]

I thought it was asking what point on the unit circle had the same point as a point on the line of sqrt(x). I know, I know, the question didn't explicitly mention it, but I assumed because of the word "quadrant", I think that threw me off

Am I only worrying about the sqrt(x)?

[shadow summit]

You understanding of the question is incorrect. A quadrant means the positive/negative values of x and y (google Cartesian plane quadrant). And you are trying to find the slope of a point passing through y = sqrt(x).

[tender mist]

So any point, in general?

As long as it's in that quadrant, on that line?

[shadow summit]

Yes

[tender mist]

Okay, thanks, that simplifies what rubbish I was trying to assume it meant, lol

That should be good, I think I know what to do now

[shadow summit]

The first quadrant is whenever the x and y values of a point are both positive (in this case every point you are working with should lie in the quadrant).

[tender mist]

Right. I just never heard that term outside of trig when I used to go to high school, so I always treated it as a "trig term"

[shadow summit]

Understandable.

[shadow summit]

If you need any more help I’ll probably be around

[tender mist]

Aighty thanks. I should be fine for now. I'm actually not looking at a pre-calculus textbook, I'm doing calc, but I'm in the first chapter which consists of pre-calc stuff, so I'll probably stick around here for now

Actually one more thing. What is meant by a "natural domain"? I don't think that term ever showed up where I went to school. I know about domain, but I don't know what a natural domain is

[shadow summit]

Well the domain is what you set it as, and the natural domain is what is defined by the essence of the function. Take f(x)=sqrt(x) for example. It’s domain is everything in the first quadrant, not because you defined it as that, but because that’s just how the function is.

[tender mist]

So depending on the question, they can mean exactly the same thing, if there wasn't a domain restriction, since natural domain has no restrictions except what the function itself has. Gotcha

I figured that's what it was, but I was confused, lol

[shadow summit]

Don’t worry, you might not be used to how some text books say or do things.

My teacher absolutely hates a certain textbook because of how it says stuff.

[tender mist]

Yeahh, I think my schools always had their own sources, so I'm not familiar with math textbooks in general

[shadow summit]

I got used to it cuz I used 3 different text books.

[tender mist]

Dang, nice. Right now I'm using Thomas' Calculus book. I know this covers like 3 courses in 1 book, but it should still be helpful anyway

[shadow summit]

Nice, might check it out.

[tender mist]

Far as I know, it covers calc 1 to 3

Or mostly

Over 1000 pages

[shadow summit]

Well, I’ve got some time to kill later today. I’ll get a start on it so I don’t feel lazy.

[whole spruce]

can someone help me find the phase shift of this cosine graph

[unkempt drift]

can any one solve this

[brisk adder]

There is none or it depends really

[warm oyster]

$\int \rm{x^n dx}= \rm{nx^{n-1}}$

[obsidian monolith]

ഴajat

[warm oyster]

and then put the limits

[unkempt drift]

ok thanks

[whole spruce]

yes, youre right! there is none.

[delicate bloom]

No, that’s the derivative instead

[scenic coral]

Yea that's just wrong

$\text{power rule}\ \int x^n dx = \frac{1}{n}x^{n+1} + C\ \text{and then use fundamental theorem of calculus} \ \int_{a}^{b} f(x)dx = F(b) - F(a) \ \text{where b > a and F(x) is the antiderivative of f(x)}$

[obsidian monolith]

someone1010

[stuck harbor]

are the vertical asymptotes 4 and -3

it says it’s only 4 on mathway

but i think i’m supposed to plug in -3 and 4 on the number to find the limits

[scenic coral]

That is correct

If the binomial cancels in numerator and denominator you get a point discontinuity rather than a vertical asymptote

Ex: (x+1)x/(x+1)

,w graph (x+1)x/(x+1)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by someone1010

[scenic coral]

notice that there is no asymptote

[stuck harbor]

yes

why though

[scenic coral]

Well, a/a = 1

[stuck harbor]

yeah

[scenic coral]

It doesn't go to inf bc it cancels

[stuck harbor]

how do i know that it is only 4

is because the x+3 already cancels out

[scenic coral]

Not sure how to rigorously prove, but 4 doesn't cancels so it makes an asymptote, though that's not a satisfying explaination

[stuck harbor]

ok

[stuck harbor]

so in other words is this right too

[scenic coral]

Probably

[stuck harbor]

ok thx

on the number line would it also just be testing the 3.9 and 4.1

[untold adder]

Is this the notation of a primitive function ?

[summer ruin]

it's second derivative

[untold adder]

Thanks.

[warm oyster]

oh yea lmao didnt noticed that lmaooo

[lunar creek]

Total number of calls:
We know that the average number of calls per hour is 30. Therefore, the total number of calls in 150 hours follows a Poisson distribution with parameter (\lambda = 30 \times 150).
Number of men in calls:
Since 60% of the calls are made by men, we can consider the number of men in 150 calls as a binomial random variable with parameters (n = 150) and (p = 0.6).
Waiting time for reward:
The time between calls follows an exponential distribution with parameter (\lambda = 1/30) (since there are on average 30 calls per hour). So, the total time elapsed before the 100th call arrives is a sum of 100 exponential random variables.
For calculate these probabilities, we use the approximate Poisson distribution for the sum of independent random variables. The Poisson distribution can be used when the number of events is large, and the probability of success for each event is small.
In detail, you can use the Poisson distribution approximation for a binomial random variable when the number of trials (n) is large and the probability of success (p) is small.
For the first point, you want to find the probability of having at most 75 men in 150 calls, we can use the binomial distribution.
For the second point, we want to find the probability that the waiting time for the hundredth call is at least 3 hours, we can use the Poisson distribution.
@viscid thistle

[obsidian monolith]

☆⃞゙۪ ᪤hiִgh࣪nᧉ͟s̲s: 🫶🏻 𝖨𝘇𝗓𝕪 ܲ 𖧪

[lunar creek]

[ P(X \leq k) = \sum_{i=0}^{k} \binom{n}{i} p^i (1-p)^{n-i} ]

• ( n = 150 ) (total number of calls)
• ( p = 0.6 ) (probability of a call being made by a man)
• ( k = 75 ) (maximum number of men)
  Calculate is
  [ P(X \leq 75) = \sum_{i=0}^{75} \binom{150}{i} (0.6)^i (0.4)^{150-i} ]
  For the second point, you use the Poisson distribution to calculate the probability that the waiting time for the hundredth call is at least 3 hours. The formula is:
  [ P(T \geq 3) = 1 - P(T < 3) ]
• ( \lambda = 1/30 ) (rate of calls per hour)
• ( T ) is the sum of 100 exponential random variables with parameter ( \lambda )
  Calculate is
  [ P(T < 3) = \sum_{i=0}^{299} \frac{(1/30)^i e^{-1/30}}{i!} ]
  In the end:
  [ P(T \geq 3) = 1 - P(T < 3) ]

[obsidian monolith]

☆⃞゙۪ ᪤hiִgh࣪nᧉ͟s̲s: 🫶🏻 𝖨𝘇𝗓𝕪 ܲ 𖧪

[lunar creek]

@viscid thistle @wanton thicket

Oh sorry I tag you accidentally Priuz

[viscid thistle]

thank you very much, will look into it

[lunar creek]

Np

[viscid thistle]

can you also explain the second one?

[lunar creek]

Sure

You can use those methods:
• Method of Moments:
The method of moments uses sample moments to estimate the parameters of a distribution. In the case of an exponential distribution like this one, the first sample moment is equal to the expected value of the distribution. So, we need to equate the first sample moment to the first theoretical moment. For the exponential distribution, the first theoretical moment is ( \frac{1}{a} ).
Calculate the first sample moment (( \bar{X} )) and solve for ( a ):
[ \bar{X} = \frac{1}{a} ]
[ a = \frac{1}{\bar{X}} ]

• Maximum Likelihood Method (ML):
The maximum likelihood method finds the value of the parameter that maximizes the likelihood function. For the exponential distribution, the likelihood function is given by:
[ L(a) = \prod_{i=1}^{n} a^2x_i e^{-ax_i} ]
It's often more convenient to work with the logarithm of the likelihood function (log-likelihood):
[ \ln L(a) = \sum_{i=1}^{n} [2\ln(a) + \ln(x_i) - ax_i] ]
Take the derivative with respect to ( a ) and set it equal to zero to find the value that maximizes the log-likelihood.

[obsidian monolith]

☆⃞゙۪ ᪤hiִgh࣪nᧉ͟s̲s: 🫶🏻 𝖨𝘇𝗓𝕪 ܲ 𖧪

[viscid thistle]

thank you very much

[warped cipher]

How's this precalc

[viscid thistle]

thats what im fuckin sayin

technically 1+1=2, is pre calc

[warped cipher]

read the channel's description

not that basically

[viscid thistle]

is it before calculus: yes

[shadow creek]

How do I set this up I can't figure it out

[shadow creek]

<@&286206848099549185>

[candid gale]

matrices- my enemy-

[shadow creek]

Can u help me please

I tried already but I don't know if it's right

[shadow creek]

What'd i do wrong

[shadow creek]

<@&286206848099549185>

[shadow summit]

what are you plugging into your calculator? and what is the problem, is it the negative? perhaps one of your assumptions is wrong.

[blissful pier]

can anybody help me with understanding the basics of transformations, translations, and dilations of a linear function?

[solemn shore]

Use desmos

When 2X replaces X, less of a value is needed to replace Y value

Hence graph is factor of 1/2 along X axis

[lapis sable]

bro

rotate graph

[shadow summit]

what are you using to transform the line? are you using matrices or just calculus?

[proper zodiac]

what are the cosh and sinh functions for, i know they exist but i’ve never seen them be used

[wraith hawk]

<@&286206848099549185>

Idk were to start with that

[sinful moth]

Halloo

How do you convert to general equation an ellipse thats equal to 0.5 not 1

[summer ruin]

multiply by 2?

if you meant to say equal to 1 and not 0.5

[sinful moth]

It doesnt workk

It shows different answer

x^2/(3sqrt(2)/2)^2 + (y + 21/5)^2/(3sqrt(2))^2 = 1

,help

[obsidian monolith]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[sinful moth]

x^2/9+(y+4.2)^2/36=0.5

[odd cloak]

HELP Please

[viscid thistle]

wut is the problem?

[odd cloak]

the answer

;-;

[viscid thistle]

n=3

[odd cloak]

how

[viscid thistle]

n=7 too

n=11 too

[odd cloak]

;-;

depression

[viscid thistle]

n=15 too

ok

[odd cloak]

brains not braining

[viscid thistle]

n=19

n=23,27,31

ok done

idk why my butt is itching and i see the form 2^(3n)-3^n being divisible by 5

[odd cloak]

finding n wasnt the question

;-;

[viscid thistle]

sorry i am bit drunk today

i scratched my butt and for n=3+2k for k>=2 and k=0 agrees

[kindred egret]

Is anyone good at logarithms and exponentials?

[shadow summit]

Don’t ask a question like that. Just post the question you are resale trying to ask. Otherwise you will probably not get a response, and even if you do get a response you will have to follow up with another response to ask the question you initially wanted answered.

[kindred egret]

My apologies I have it posted I've just been patiently waiting

[shadow summit]

Well what’s the question?

[kindred egret]

It's in the channel help 37

[shadow summit]

Can you link the channel?

[kindred egret]

#help-37

[real cloud]

can anybody help me

[shadow summit]

just post the question bro

i swear, people just be asking for help instead of just asking the question.

[real cloud]

the part below it is what i got so far

[shadow summit]

note: sqrt(3)/3 = 1/sqrt(3)

are you aware of exact value triangles?

[real cloud]

bro i spent 20 minutes just to get that too😭

[real cloud]

no im supposed to be by this point tho

[shadow summit]

They are pretty easy to learn, and they are basically the holy grail of trigonometry.

arctan(1/sqrt(3))=60 degrees.

x+135=60

x=60-135

x=-75

[real cloud]

are there any more answers or is it just -75

[shadow summit]

if it didnt ask for anymore solutions than you dont need any more.

[real cloud]

its between 0 and 360 degrees so there can be multiple answers

[shadow summit]

Not that I've heard of before.

[shadow summit]

Figure it out if you think there are more answers.

They have exact values for the side lengths of triangles with interiors 45-45-90 and 30-60-90

i said exact value triangles.

huh, ive never heard of them being refered to as anything different, neither in text books, youtube videos or from teachers.

they arent really special, other than the fact that they have some of the most commonly used angles in them, and easy to represent side lengths.

Well all triangles have constant proportional sides.

take a right angle triangle with interior angles 15 and 75.

Set one of the side lengths equal to 1.

Solve for the remaining sides.

bam, proportional triangle.

What makes it proportional then?

yes, the triangle i have just created has all 3 sides being constants.

you do know what a constant is, right?

I made them the constant, therefor anything that shares the same angles will be proportional to the triangle i made.

They just have commonly used angles.

[real cloud]

tanx/secx simplified is sin x right

[shadow summit]

Yes

[real cloud]

Did I do this right

1 is the answer I got

[kindred egret]

I have a question: what are all the rules for logarithms and exponentials?

[shadow summit]

This is correct.

[kindred egret]

Thank you, and which one would be the one you mentioned before? It was like a^log_a(x)=x

[shadow summit]

those arent all the log laws, but you should be able to do all questions using them.

[kindred egret]

Oh

[shadow summit]

here are a few more

[kindred egret]

Thank you

[jolly harbor]

M and N must be positive factorial

[shadow summit]

it says that in the second image, the one you replied to.

[jolly harbor]

I’m making a joke with ! And factorial

[shadow summit]

oh

im too tired to realise

dammit

i should have picked up on it, i love those kinds of jokes.

[severe musk]

how does one do these 😭

anybody here 😭

[shadow summit]

It’s just a trig function. Tan(31)=450/x

[kindred egret]

With systems of linear equations, what do you do when you get 0 = 0?

[shadow summit]

It means you’ve messed up.

Try dividing the entire equation by a constant (hint:||3||)

[kindred egret]

Which equation?

[shadow summit]

3x+9z. It’s the only one I can see, so there might be an easier way to go around solving it.

[kindred egret]

I'm trying to find x,y,z

At this stage I would find out what x was but it becomes zero?

The calculator says I get
z=z
x=0-3z
y=6+z

But idk how

[shadow summit]

I don’t have a piece of paper on me rn, but start by doing equation 2-3(equation 3)

[kindred egret]

You're saying 2-3 then plug that into equation 3?

That gets me 0 = 0 I've tried

[shadow summit]

Solve for y and z first.

Do you know how to calculate where two lines meet?

[kindred egret]

Yes, using elimination I got 0 = 0

[kindred egret]

Huh

[shadow summit]

Check back in your working out, are you doing -(eq3), remember into distribute the -1 onto all terms?

[shadow summit]

Because if you focus on eq2 and eq3 by them selves, it is the same process for finding the values of y and z.

[kindred egret]

So I do
-(y-z)=6?

I get -y+z=-6

What i do with this

[shadow summit]

Multiply it by 3 giving you -3y+3z=-18

Then add the second and third equations together

[kindred egret]

That make zero?

[shadow summit]

No it doesn’t.

Wait

I’m getting confused with something else

[kindred egret]

-3y+3z = -18
3y -3z = 18

0=0

[shadow summit]

Lemme just go do this on paper rq

[kindred egret]

Okay

Appreciate it

Considering one of the equations I got was x+3z=0, and the calculator says x is supposed to be 0-3z, it looks to me I'm supposed to get x by itself? But why

And how does z=z

[shadow summit]

Does this question come from a textbook?

[kindred egret]

Nope

[shadow summit]

So you created it?

[kindred egret]

No

[shadow summit]

Where’s this question from then?

[kindred egret]

It's a practice question generated from a professor

[shadow summit]

Uhhh

[kindred egret]

On Cengage I think it called

I can just put my help in a help channel

[shadow summit]

Maybe don’t trust that website.

It’s not possible.

[kindred egret]

But the calculator provides answer

[shadow summit]

What does calculator give you?

[kindred egret]

X = 0-3z
Y = 6 +z
Z = z

[kindred egret]

I was saying here

[shadow summit]

Wait

[kindred egret]

Ok

[shadow summit]

You’ve got 5 equations?

[kindred egret]

I made the next 4 and 5

[shadow summit]

Huh

[kindred egret]

3 were the question part

[shadow summit]

Are you trying to find z?

[kindred egret]

I'm trying to find x,y, and z

[shadow summit]

Yeah you can’t find z.

It’s impossible.

[kindred egret]

Yeah but what is the reason we write the answers like that

[shadow summit]

When I say “find z”, I mean like, it’s value (4, 19, 3.14, ect)

And if the calculator just says z=z, that means it’s impossible.

[kindred egret]

I see so since I got 0 = 0 it's impossible to find z and we have to write x and y in a different way

?

I think it's like you have to write x and y in relation to z

[shadow summit]

Put it this way, it’s like trying to the intersection point of two lines, but the they are the same line. So there is no single intersection point.

[kindred egret]

Yeah

[shadow summit]

That means the value of z does not exist.

[kindred egret]

What abt x and y

[shadow summit]

Well considering how we can’t solve for x or y without using z, it means that they are also impossible to find.

[kindred egret]

Oh

[shadow summit]

This happens because eq2 and eq3 are just the same equation.

[kindred egret]

but the calculator gave an answer?

[shadow summit]

No

[kindred egret]

No?

[shadow summit]

I used a calculator to check if there were any solutions and it basically just said it impossible.

[kindred egret]

Is my calculator wrong or smt I'm confused

[shadow summit]

Well it tells you x=-3z, and because there is no value for z it is impossible.

[kindred egret]

Oh I got it right

Problem solved

Thanks mate

[willow skiff]

the two roots can be the same

you're missing the part "counted with multiplicity"

so (x - 0)^2 tells us that x = 0 is a root with multiplicity 2

[solemn notch]

Does anyone have a roadmap or website I can follow

To learn pre calc and calc

Properly simply and correctly

Without confusing shoot

Like excsersises and stuff toowebsute

Too website*

[willow skiff]

https://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx

Paul's Online Maths Notes

[zenith vapor]

Help me pls

[viscid thistle]

OMG I thought I got banned for no reason.

[shadow summit]

What is the question asking?

[clever dock]

Someone give me any clue about what to do please. I don't even know where to start lmao.
The exercise asks to develop (1+n)^n with Newton's binomial and derivate the result of that in order to prove those identities.
Any clue would be very helpful

[light forge]

Did you start off by developing (1+x)^n ? If so what did you get?

[clever dock]

I tried to develop it as the sumatory definition of the newton's binomial, and when I tried to derivate it I almost got the first identity, but it wasn't so easy. This is what I got

I probably have made an error, but idk where

the other stuff I have are just random calculations in case I came up with sth, but that led me to nowhere

[shadow summit]

the original question starts with k=1, not k=0.

[shadow summit]

cant you use proof by induction?

[clever dock]

Yeah I know, that was one of the things I was not sure about what to do

[clever dock]

Probably that's the method to get the answer right, but tbh, we haven't used so much induction, so I would still don't know where to start lmao

[shadow summit]

Expand the sum and it will make proof by induction very easy.

[shadow summit]

You are trying to prove the binomial theorem correct?

Anyways, I can’t help rn, I’m on my phone. I would’ve helped earlier though but its 12am now.

[clever dock]

I'm trying to, by developing (1+x)^n amd derivating it, prove the two identities shown in the image, I don't think I have to prove the binomial theorem

I'm not sure but I think it supposes that it has been already demonstrated

[clever dock]

Don't worry, I'll try sth, thanks a lot

[viscid thistle]

ni

ce

[whole void]

haven’t taken precalc yet

but if find f(0)

u gotta evaluate 1/2 + 2/4 + 3/8 + 4/16 + …

which is two and there’s only more choice that matches up to this

[grim maple]

aankho se tune ye kya keh diya

dil ye deewana dhadakne laga

[viscid thistle]

How do you draw this?

I get an absurd number

[shadow summit]

How accurate do you want your graph to be?

Because you can jus make a table of a points that lie along the graph.

If that’s the level you are at

[viscid thistle]

Hmm would that matter?

I have a question that’s kinda irrelevant to that i think

basically The height of a tree in centimeters t years after it was planted, is given with the function shown

Then I need to determine grapgically the momentary growth rate after 10 years

[viscid thistle]

very accurate

[shadow summit]

Honestly, I forgot how to do this without derivatives.

So if you are at the level where you can use derivatives and set the equal to 0, just use the first derivative to find the turning points, the second derivative to find the inflection point, and then just plug all those bales back into h(t).

But if your not at that point, idk.

[viscid thistle]

😭

and there goes my help

I’ve tried deriving

[shadow summit]

Sorry mate

[viscid thistle]

let’s just say it went horrible

this midterm went HORRIBLE

I’m so far behind it’s outrageous

[viscid thistle]

I need to factorize before deriving no?

[shadow summit]

$h’(t)=-\frac{1}{10}t^{2}+5t$

[obsidian monolith]

TheLord26

[viscid thistle]

Wha…

How did it come to that conclusion?

[shadow summit]

Set h’(t)=0 to find the x value for the turning points.

[viscid thistle]

oh God…

[shadow summit]

That is the first derivative.

[viscid thistle]

I’m so tired rn

[shadow summit]

Bro this is my 2nd day without sleep and I just did a derivative in my head. I am relying on autocorrect to not mess up.

[viscid thistle]

Yes but you’re an undergraduate or a graduate 😂

a math major perhaps

I’m a preuni student

[shadow summit]

Don’t have school rn.

[viscid thistle]

also why tf would you torture yourself 😭

Sleep!!!

Are you trying to hallucinate?

[shadow summit]

Well I can’t sleep now, it’s 6:17am

[shadow summit]

Been there done that.

Not fun.

[tranquil gull]

What are you studying

[shadow summit]

This is a precalc channel, so precalc ig?

Anyways I’m going I don’t have the mental strength for math rn.

[viscid thistle]

algebra to calculus

and physics

[tranquil gull]

Lol sorry im new

Not new actually

[tender quest]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[untold adder]

Use this property, and you'll find the answer.

[restive carbon]

whats good to study for a pre cal test ?

[uncut mulch]

algebra, functions, geo, trig, exponents, logs

[willow skiff]

the stuff in here

https://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx

[near viper]

can someone explain?

[willow skiff]

which part?

[near viper]

part a pleawe

[hushed sphinx]

Compute the first few terms by hand -- do you see a pattern?

[near viper]

grows by 2n

[willow skiff]

really? that would mean the population after 1 hour would be 2,200

[near viper]

oh 2 to power of n

right:

[willow skiff]

stop guessing

[willow skiff]

you forgot to take away 1,000

[near viper]

(1110)2^n-1 -1000

[willow skiff]

how many are there after 1 hour?

[near viper]

wait nvm it would be 1200

[willow skiff]

yes

[near viper]

then 1400

[willow skiff]

now how many would there be after 2 hours?

[near viper]

cuz only 100 doubles i think

[willow skiff]

yes

mb

yeah

and then one more time to see the pattern?

[near viper]

1800

thanks alot btw

[willow skiff]

yeah nw

thank Tropo as well

[viscid thistle]

yo

can someone help me with precalc?

[tropic coyote]

what is it

theres a 50% chance ill be able to help

[viscid thistle]

ok

so it has to do with derivatives

which I don't have a problem with

the problem is the fricken equation

that has a cube and a square

with a fraction

[tropic coyote]

alright can i look

[viscid thistle]

i'll just show you here

[tropic coyote]

maybe i can help

[tropic coyote]

oh that

[viscid thistle]

t is 10

[tropic coyote]

so what are you meant to do with it

set t=10?

[viscid thistle]

I get 216.666, but I can't derive it cuz the factor is hard

[viscid thistle]

I should find the growth rate at t = 10

[tropic coyote]

oh

just find derivative and set t=10

wait let me solve it first so i can help

will take like 2 minutes

[viscid thistle]

I did that, but no avail

[viscid thistle]

lim
t --> 0 no?

[tropic coyote]

nah
lim
h->0

[viscid thistle]

that's the limit value of deriving for growth rate

[viscid thistle]

yes but t is h in this case

[tropic coyote]

i mean you could say so

[viscid thistle]

wait...

[tropic coyote]

but i would like to keep the 2 variables separate

so they dont get mixed up

[viscid thistle]

t is x in this case, and I wanna find the growth rate at x = 10

[tropic coyote]

yes

[viscid thistle]

so where the heck am I making an error?

[tropic coyote]

it isnt h

can i see your work

[viscid thistle]

alright

but I've done multiple pages of it

lol

[tropic coyote]

i got 40 as value

[viscid thistle]

HOW?

[tropic coyote]

wait let me graph it to see if im right

[viscid thistle]

That's the correct answer but i couldn't come to that conclusion

[tropic coyote]

oh

alright so you did it with limits right

[viscid thistle]

yes

so wait

I seriously don't understand, did I mix up the wrong variables?

[tropic coyote]

i mean if you thought of t as h then

theres a signifcant chance of it

sorry

[viscid thistle]

I wrote

lim
t--> 0

was that wrong?

[tropic coyote]

yeah

[viscid thistle]

💀

[tropic coyote]

t is supposed to be what youre inputting into the derivative

not the difference thing in the derivative

[viscid thistle]

wdym

[tropic coyote]

like

[viscid thistle]

Ohhh

I see

[tropic coyote]

oh i was about to rewrite

[viscid thistle]

I wrote delta T, as in the change in T

but it's not delta

it's just t

t = 10

[tropic coyote]

yes

[viscid thistle]

man...

[tropic coyote]

and you have to use another variable as variable -> 0

[viscid thistle]

yes I have to use 10

as t reaches 10, y reaches 40

[tropic coyote]

nah you dont have to pull a limit trick