precalculus

[pure flax]

I do now

I just don’t know how to find the value of the theta

Ø

[viscid thistle]

oh so the sin(theta) = 3/7?

Just use a calculator

[spring thunder]

@pure flax it's called trigonometric equations

[viscid thistle]

.......

[main geyser]

At my school district, they don’t have summer classes for math, and they don’t really recognize out-of-school programs for summer classes as ways of getting credits

[slender river]

most tragic indeed

[night finch]

@pure flax to find angle from given trig function use inverse trig functions

[pure flax]

ok thanks

[livid cedar]

hey im starting uni next week, and im behind on my precal stuff, but i dont even understand any of it

currently im working on rational functions and asymptotes

and it makes literally no sense to me

and i still have to do 31 more modules

[fading token]

Good luck man

[hybrid wave]

lol

[viral imp]

Hi, I'm trying to sketch this function

= tex y=\ x\sqrt{\frac{2\left|x\right|-x^2}{x^2}}

[viral imp]

although the result should be this:

https://cdn.discordapp.com/attachments/407885031315341314/480670866934333450/Screenshot_from_2018-08-19_11-33-39.png

I'm getting this:

https://cdn.discordapp.com/attachments/407885031315341314/480673346787475457/Screenshot_from_2018-08-19_11-44-07.png

[eternal folio]

sqrt(x^2) = abs(x)

That is the mistake.

[viral imp]

I'm having issues on performing calculations when |x|<0

[eternal folio]

$$ \sqrt{x^2} = |x| $$

[viral imp]

I've been told this but I don't get how to contextualise

as far as I understand, this funciton implies two cases: 1) |x| = x and 2) |x| = -x

why should I change the sign of other Xs in the function?

[eternal folio]

$$ \sqrt{\frac1{x^2}} = \frac1{|x|} $$

[eternal folio]

Do you see now the algebraic mistake you made?

[viral imp]

= tex \sqrt{x^2} = x

[eternal folio]

No

[viral imp]

this is what I always thought

[eternal folio]

This is false

$$ \sqrt{(-3)^2} \ne -3 $$

[viral imp]

oh darn got it, it is false because for instance, both -2 and 2

would lead to the same result right?

[eternal folio]

It is false because they would lead to different results.

[viral imp]

yeah, I explained myself wrong

[lost pawn]

$$(-3)^2=9$$

[viral imp]

= tex \sqrt{x^2} = |x|

[eternal folio]

Yes

[viral imp]

therefore this does always apply, and in this case

regardless of the absolute value on the numerator

[eternal folio]

Yes

[viral imp]

great. thanks very helpful!

[livid cedar]

my parents are allowing me to take calc next semester since i cant figure this out

thank you to anyone who helped me, it was very much appreciated

[thick raptor]

?

[viscid thistle]

yw

[thick raptor]

oi that's my line

[slender river]

yw

i mean thanks

[reef dirge]

yw

[weak dawn]

so, I just come back to math class and forget how to do math with calculator. I need help about how to use calculator to solve log 10 x = -2
like
how do I enter x?
and "= -2"

[tacit bay]

I don't know if calculators even allow it

And you'll probs need like a college calculator or something

Anyways x=10^-2

If you need that lol

[gilded jewel]

Just use the basics to convert it.
Eg: log2 8=3 <=> 2^3 = 8

That on a normal calculator. If you have a scientific one there is no way it doesn't have log. It may be clunky to use tho, something like

LogBase(Ecuation) => log2(8x+4)

[olive meteor]

what is simplified x divided by (x+1) also divided x^3

x

__

x+1

x^3

[spring thunder]

$$\frac{x}{\frac{x+1}{x^3}}$$ or $$\frac{\frac{x}{x+1}}{x^3}$$?

[olive meteor]

yup that

[spring thunder]

"that" which one lol?

[olive meteor]

My bad

well they are kinda the same so

So ethier one honestly

[spring thunder]

they're not

[olive meteor]

I feel stupid

Whats the difference exactly?

[spring thunder]

ok so let's just take a,b and c for the moment

[olive meteor]

alright

[spring thunder]

$$\frac{\frac{a}{b}}{c}$$

[olive meteor]

Oh I see

[spring thunder]

would be a divided by b then divided by c

so a/(bc)

[olive meteor]

Gotcha

then I meant the one on the right

Cause x^3 is the integer thats dividing the fraction

maybe thats my mistake

Im getting too many different answers on too many different sources

so I want someone to guide me thru it so I can see if Im doing something wrong

[spring thunder]

ok so now from my a,b,c thingy i did

how can you write the big fraction with only x as numerator?

[olive meteor]

okay so the problem is

f(x) x/(x+1) g(x)=x^3

(f/g)(x) what is the domain of (f/g)

[spring thunder]

ahh

usually when you have some domain problems don't simplify

cause simplifying can cause the domain to change

[olive meteor]

well I mean I am double dividing

techincally

[spring thunder]

yeah

[olive meteor]

Im not sure if I leave as it is

[spring thunder]

you can leave it as is

[olive meteor]

Okay

[spring thunder]

just worry about the denominators (small one and big one)

what are the conditions on the denominators so that f/g is defined?

[olive meteor]

all real numbers except 0

I keep getting weird answers like x^4/x+1

I got x/x^4-x^3

[spring thunder]

better to leave the den as x^3(x-1)

[olive meteor]

oh then the answer is all real numbers but 0 and -1

[spring thunder]

0 and 1

[olive meteor]

oops

[spring thunder]

it's x+1 mb

so you're right

[olive meteor]

oh okay

Thanks for the help

now to go struggle on the rest of the homework

[spring thunder]

np and gl^^

[fair osprey]

Average rate of cahnge of the function y=(1/2)x^4 + x^2 - 3 between x=0 and x=2. I've tried and I keep getting 20, which isn't one of the available answers.

[eternal folio]

The average rate of change of a function between a and b is the average value of its derivative between a and b. The average value of a funtion is incidentally its integral from a to b divided by b-a. The integral of the derivative is the function itself.

[lofty raft]

Differential Calculus
Related rates
2. The radius of a cylinder is increasing at a rate of 1 meter per hour, and the height of the cylinder is decreasing at a rate of 4 meters per hour. At a certain instant, the base radius is 5 meters and the height is 8 meters. What is the rate of change of the volume of the cylinder at the instant?

[eternal folio]

$$ avg_f(a, b) = \frac{\int_{a}^{b} f(x) dx}{b-a} $$, therefore $$ avg_{y'} (a, b) = \frac{\int_{a}^{b} y'(x) dx}{b-a} = \frac{y(b) - y(a)}{b - a} $$

[eternal folio]

Which is incidentally the slope of the line connecting (a, y(a)) and (b, y(b)).

[thick raptor]

oof overkill, just use mean value theorem for derivatives

[eternal folio]

But how does that tells us the average rate of change?

[thick raptor]

Literally the result you get without integrals

=tex {\rm avg}=\frac{y(b)-y(a)}{b-a}

[fair osprey]

To sound like a spud, what's a intergral?

[eternal folio]

Wow I didn't know that... I thought the mean value theorem asserts the existence of a point c such that $$ f'(c) = \frac{f(b)-f(a)}{b-a} $$ (conditions omitted).

[thick raptor]

this is what you get @eternal folio for doing that lol

Well it's called the mean value theorem for a reason

[eternal folio]

I guess it makes sense

But how would you solve this without calculus? It's the #precalculus channel, after all.

I don't know why I wrote that integral solution.

[thick raptor]

You don't need any calculus 🤦

just [y(b)-y(a)]/[b-a]

[eternal folio]

Guess I am stupid, but why is that the average rate of change?

[thick raptor]

:l u literally just proved it using the mean value theorem for integrals

[eternal folio]

You don't need any calculus 🤦

so how do you prove without calculus?

[thick raptor]

You don't prove things in precalculus

doh

[eternal folio]

wat

[thick raptor]

xD

dw about it

[eternal folio]

Then I guess, @fair osprey, that you have to accept that it's (y(b) - y(a)) / (b-a).

[fair osprey]

@eternal folio @thick raptor thanks to both of you ❤

[thick raptor]

@lofty raft you do realize there's a calculus channel

[lofty raft]

Maxima/Minima
Problem Set

1. A rectangular lot of fixed area is to be fenced and divided into three by parallels to one of the sides. What dimensions would minimize the amount of fencing used?

[eternal folio]

The perimiter P(a, b) = 2a + 2b + 2a, given that ab = area.

Assuming that the length b side will be divided into three parts.

[hexed ermine]

Yeah, I thought average rate of change usually shows the secant line of a function while instantaneous rate shows the tangent line, just use your elementary slope formula to find the average slope between the two points

Oh nvm didn't realize this was a day old lel

[lofty raft]

2nd derivative of y=xsinx?

[hexed ermine]

Hmm 1st derivative would be xcosx+sinx, derivative of that is cosx-xsinx+cosx giving you a 2nd derivative of 2cosx-xsinx

[lofty raft]

how come?

Find y^1
a.) sin(x+y)+sin(x-y)=1
b.) ysinx + xsiny = 5

[eternal folio]

=pup {sin(x+y)+sin(x-y) = 1, ysin(x)+xsin(y) = 5}

[granite stirrup]

Do more with Wolfram|Alpha pro

Query made by

@eternal folio

[eternal folio]

Lul

[lofty raft]

huh?

[trim coyote]

How do you guys recommend notation in Discord?

Writing the syntax for math equations kind of sucks.

[lost cipher]

latex?

[trim coyote]

Appreciate it

[kindred violet]

I'm taking pre calc rn and calculus. which calculator would you guys recommend? TI 84 or TI 89 titanium?

[true vigil]

hands

[cloud cedar]

g(x)=3(x-4)^2-11 find (g(a+h)-g(a))/h

[haughty thicket]

@kindred violet ti nspire CAS its a little pricy but it can do EVERYTHING

[copper hatch]

@kindred violet it might not be allowed everywhere tho

the cas that is

[hexed ermine]

84 @kindred violet 99% of ppl accept it

[fickle moat]

I have aquestion that i been stuck on this question for good 2hr. I need help.

Can someone tell me where i messed up..

[wind igloo]

You go from 1,000,000 = 473.5827 y^(5/2) to 999,526.4173 = y^(5/2)

That isn't a valid operation. You subtracted on both sides when I think you needed the divide.

@fickle moat

[prisma scroll]

=pup 1000000/473.5827

[granite stirrup]

Do more with Wolfram|Alpha pro

Query made by

@prisma scroll

[stray obsidian]

130

how would i go about tackling this problem

[prisma scroll]

just factorising?

[stray obsidian]

do i bring the negatives to the bottom?

i think its the fractions giving me a hard time

[prisma scroll]

try taking

$$ \frac{\sqrt{3x+4}}{x}$$

[prisma scroll]

take this as common

and see what you get. that should work out

[stray obsidian]

im pretty sure i did it completely wrong but is the solution (3x+4)(2x^1/2 +4)

yea my factoring isnt that good

[harsh yacht]

Not really sure why that is the solution since that can be factored further into

2(3x+4)(x^1/2+2)

[stray obsidian]

oh dang

[slender river]

oof

[neon vale]

PLEASE HELP IM IN COLLEGE PRECALC AND CANT DO THIS SHIT

[slender river]

mathxl is g0y

i hate it so much

anyway

you have to use pythagorean theorem to get distance

imagine two points on a plane

there is a straight line to get to them

i mean to get from point a to b

[neon vale]

Yeah I got the distance formula but how do I even solve it when x>0

It could be any number above 0

[slender river]

dont worry about that?

you can leave x in

it should still hold for all x's

i got an answer but i want to hear yours first

[neon vale]

Ok wait im solving it

[slender river]

coo

[neon vale]

Uhhh is it 5x lol

[slender river]

yeah

nice job!

[neon vale]

Thank youuu

[pearl peak]

Stefan Karl dies
Internet: 😪

Sen John McCain dies:
Internet: who?

[slender river]

lmao

[viscid thistle]

So I’m taking precalc rn

Any advice to do well in the class?

[slender river]

memorize

that class is the worst intuitively out of all of the math classes

ask questions

[thick raptor]

ew

[slender river]

ya

[earnest brook]

@viscid thistle don't memorize* it, if u mean trigonometry is a concern, just draw the unit circle and see the relationships that come out of it. PatrickJMT, 3Blue1Brown, and your textbook ofc are good resources you should check regularly

🙏

[slender river]

yeah that caveat i forgot to mention

like actually learn but there's stuff you need to know for a long time

like material wise

[stray obsidian]

How would i rationalize the left side of question 120

multiply both sides by 3/2? or 2/3?

[earnest brook]

u mean

raise both sides to the 3rd power

that will get rid of the cube * root

[stray obsidian]

oh ok cool

i thought there was an imaginary two on the side

since thats how u fet rid of it normally

[earnest brook]

well

this is not a square root

its a cube root

remember the basic exp rule

[stray obsidian]

ok cool thanks

[earnest brook]

$$ (a^b)^c = a^{b*c}$$

[earnest brook]

so whenever you have an n'th root

the way to "cancel it"

is to raise both sides by n

[stray obsidian]

for 135 i got the answer bu plugging in numbers

but how would i reverse it to get the answer from x

im stuck at 1250=(30-.1x^2)

[night finch]

would i be wrong to say the ultimate goal of trigonometry is to find the 3 lengths, 3 angles and 3 main trig functions of a triangle

and its all strategys to find them based on what your given

[night finch]

also, wkipedia says a vector valued function's input can be a scalar or a vector but i can't find anywhere a example with vector input its all scalar inputs and space curves

is it just like saying its possible but nobody has a use for it

is there any other known list or library for good vector valued functions beside space curves

http://mathworld.wolfram.com/topics/SpaceCurves.html

[viscid thistle]

yo

a good example of a vector valued function with a vector input would be like taking a matrix and multiplying it by a vector

vector goes in -> multiplies by the matrix, that's your function -> out comes your vector output

to answer your other question, I'd say trig is roughly about that sure

I think the main point of the trig functions is to relate all similar triangles together

since similar triangles have the same angles and similar triangles all have the same ratio of sides

it gives you a way of moving between them, but it's sort of nice to imagine the unit circle as being kind of the most important representative of a class of all triangles that are similar, or something like that

at the end of the day, I think the main use of trigonometry is to talk about circular things from rectangular coordinates

[night finch]

my man👌

genius

coming full circle (pun intended) a vector valued function is transforming a vector. aahhh...

when u say relates similiar triangles makes me imagine a tet mesh

[viscid thistle]

haha

[night finch]

working with triangles meshs...

[viscid thistle]

oh I don't know about the mesh part

when I say similar triangles I mean specifically the math definition of "similar triangles"

just wanna be sure I'm clear about what I say since it sounds like regular speech a bit

[night finch]

yea ic ill google that

[viscid thistle]

https://d2gne97vdumgn3.cloudfront.net/api/file/hLpEQAFRsqSeIPQQLmAH

so here are two similar triangles, all angles are the same and the ratio of corresponding sides are the same

6/7 = 12/14

so you can use this fact to figure out what this 3rd side should be on the bigger triangle, knowing that they're similar

[night finch]

ah ic

[viscid thistle]

same kind of thing happens when you use the unit circle when you think of doing trig, you're using that as a similar triangle to some other larger triangle

like, finding the x and y components of a vector, or something like that, knowing its length and angle

[night finch]

o ic

yea i get it thats insightful

[viscid thistle]

I think maybe the main takeaway to be as practical as possible

if you know two triangles are similar, you just need to know two sides or one side and one angle

and then you can figure out everything

[night finch]

yea

two sides = pythag

angle and hypo = polar

ad if there similiar you can deduce

[viscid thistle]

yeah that sounds about right to me

[night finch]

i think thats correct term

[viscid thistle]

just something to maybe keep in the back of your mind to relate some vector stuff to trig stuff

=tex a \cdot b = |a||b| \cos \theta \ |a \times b | = |a||b| \sin \theta

[viscid thistle]

the dot and cross product are related to sine and cosine in this way

[night finch]

oo

yea i knew the dot one

dot of two vectors is cos of angle between them

and u can arccos that to get angle

but didnt know cross is the same for sin

[viscid thistle]

yeah I guess to be pedantic, that's only true for normalized vectors

since normalized vectors would have |a|=1 and |b|=1

[night finch]

ye right

so used to work in houdini your vectors are always normalized i forget to consider it haha

[viscid thistle]

yeah haha it's pretty useful and common to normalize stuff though so that's not too bad an assumption to make by default most of the time anyways depending on what you're doing

idk I imagine sometimes it's not useful to normalize though, just extra wasted computing depending on what you want to do though maybe?

I don't know though

[night finch]

so given two vectors... with that above you could get cos and sin of angle between them..

[viscid thistle]

yeah

pretty handy really

[night finch]

and u could then rotate them both perfectly around unit circle..given there normalized..

[viscid thistle]

actually you can think of both of those operations as matrix operations too

[night finch]

I assume cant imageine the operation off the top

[viscid thistle]

but it looks kind of less dangerous if you write them as their own little operators like that

[night finch]

hmmm

[viscid thistle]

yeah you could do that

if you can imagine some kind of operation, it's a good idea to try to figure out how you'd do that with math I think

since that's how I work, I think what I want to do first, then I kind of translate that into math, although it's a little more seamless for me nowadays

like you don't want to be a bitch to the math, you want the math to be your bitch lol

[night finch]

yea for sure

if i can figure somthing out in notation before i bring it into hou that would be the day

thats my whole goal learning this stuff basically

that would be rly cool

[viscid thistle]

yeah for sure, you'll get there

I wasn't born knowing this stuff either

I remember learning trig stuff my first time no clue what this stuff was

but then once we started using it in physics I got more interested cause it was actually good for something not just useless symbol pushing

[night finch]

yea for sue

i never learned it in high school honestly

i actually asked my teacher in middle of class where i will ever use this ( i was a "bad" kid) lol

[viscid thistle]

ahahaha

I failed precalculus in highschool, that's when I had to learn it

[night finch]

now that i have application for it now im into it

[viscid thistle]

I only ever learned it in my second year of university

I self taught off with the help of khan academy cause I had application for it too lolol

[night finch]

yea traditional teaching methods fail.. kids just either just go with the flow or enjoy the puzzle aspect..

but dont even understand what there doing..

[viscid thistle]

yeah once I found my own path to what I was interested in, I just have been doing my own thing ever since

I am not a rote memorizer that's for sure, I have to do things the hard way and figure it out and understand them until I'm satisfied, so yeah I definitely respect that

too many math people especially seem content with memorizing definitions and blindly applying them to theorems, that ain't me

[night finch]

yea na im not into that

[viscid thistle]

then again that's why my degree was in chemistry, I was interested in differential equations and linear algebra to get to understanding how to derive the schrodinger equations for molecules to model their properties and absorption spectra and stuff like that

[night finch]

high level

lol

[viscid thistle]

haha a lot of bashing my head against stuff and feeling stupid for hours

I think once I did enough math though, it kind of ruined other aspects of life for me in a sense

if I don't feel overwhelmed by a lot of stuff to figure out I get kind of bored haha

I need to be like constantly in trouble haha

[night finch]

i hear ya

i brainstorm all day everyday

always on somthing..

[viscid thistle]

yeah I feel that, definitely how I operate, I'm always grinding away at some thought or something

and usually what I'm thinking about is something that people would even insult me for, like really simple sort of stuff too but I'm just not really as smart as I seem I just am constantly working I think is all it is

just the desire to understand and know why etc anyways I should probably get back on the houdini train myself now that my 10 hour days have ended officially as of this week lol

[night finch]

if ppl insult u for thinking about somthing because it it is simple they are conceited

yea i gtg 2

later man

[viscid thistle]

yeah haha

later man

[trim coyote]

How many of you are doing Pre-calc in uni?

[brave void]

Need help

What I have is find the limit of this one problem

(sin x )/(x)

[thick raptor]

It's the well-known limit that equals 1

[brave void]

wtf really

[thick raptor]

Do you need a geometric proof?

[brave void]

no no no

Just

How do I put it in my calc

[night osprey]

lol

[earnest brook]

xdd

[thick raptor]

lmfao

welp uh

[brave void]

ti 84

[thick raptor]

GL with those endeavors

[brave void]

how would I put the thing in my calc

to test different values

I have to test different values of x

And its not spitting out the right numbers

[earnest brook]

well i mean, he could graph and trace right?

if u got a graphing one

[brave void]

like I have to test -.1 in the equation

[earnest brook]

still i'd recommend what panda said of learning the geo proof

[brave void]

and -.01

[earnest brook]

then u'd just remember the limit as 1

[brave void]

I have to fill out a chart

for values around it

[earnest brook]

oh so numerical analysis

[brave void]

Yes

[earnest brook]

then ye just plug it in like that in ur calc

[brave void]

It has sin

Then is has parenthesis

what do I put in parenthesis

x?

[earnest brook]

just use a variable and have sin(x)/x , and keep rerunning it after changing x

[brave void]

I did that

I got random ass numbers

of like

.01754234

not remotely close to one

[night osprey]

sin(-0.1)/(-0.1)

[earnest brook]

[brave void]

I did that

[thick raptor]

Are you in radians?

[brave void]

Degrees

[earnest brook]

Respect.

xd

switch to rads

[brave void]

OOOOH

Ty

[thick raptor]

k

[brave void]

just

first day in calc AB*

[earnest brook]

gl 🙏

[night osprey]

good luck

[brave void]

ty ty

[thick raptor]

nice hf

[brave void]

am scared Im gonna fail lmfao

[thick raptor]

series is gud for u

always ask for helps when u needs my man

[brave void]

I got this server

^_^

[earnest brook]

just remember gabriel polynomial > taylor polynomial

[thick raptor]

[brave void]

You guys got me through half of middle and high school

[thick raptor]

t!wiki gabriel polynomial

[brisk mica]

📖 | ** https://en.wikipedia.org/wiki/Algebra **

[thick raptor]

@earnest brook wot

[earnest brook]

lemme look it up, was an article

http://thenewcalculus.weebly.com/

[thick raptor]

very confused

AFAICT the link just leads to Newton's polynomial interpolation

@earnest brook

[night osprey]

why cant i say that?

[thick raptor]

ur probs saying something that should go somewhere like #chill

[night osprey]

im responding to this new calculus thing

[earnest brook]

i'll post it in chillout

[brave void]

What is oscilating behavior

[thick raptor]

means like it goes up and down

like a wave

[brave void]

k

[earnest brook]

oof he hit u with the k

[thick raptor]

probably means that at least

k

[brave void]

guys

need help with this one too

1 sec

I dont have a phone

Number 21

Idk how to do this problem

So I know there are limits at

-3

and 2

so would the answer be those two limits?

[thick raptor]

You're looking for where the limits exist

Does it exist at -3?

[brave void]

Yes

[earnest brook]

😦

[brave void]

wait

No

It doesnt

[earnest brook]

why

[brave void]

It exists everywhere but there

but why doesnt it exist

[earnest brook]

why doesn't $$ \lim_{x\to-3} $$ exist

[earnest brook]

you said it didn't exist

[brave void]

Because there is already a point there

[earnest brook]

why

eh

[brave void]

?

[earnest brook]

no

[brave void]

because it is 2?

[earnest brook]

if u look at the graph, what is happening to the function as u go close to -3 from the right?

what value does it "want" to be?

[brave void]

0

Wait a sec

Its different values

Approaching from different sides

Making a limit null and void

Non existant

DNE

and 2 exists

Because it approaches from both sides

and both wants to meet at the same point

[earnest brook]

😃

gg

[glacial fern]

hi guys im having trouble here would be extremely grateful if anyone helps me

my teacher wants me to turn this into a sigma notation

x+(x+x^2)+(x+x^2+x^3).........+(x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)

i dont know how and this is literally breaking our class into pieces

[buoyant harbor]

Do you see a pattern

Between the terme

Terms

And a pattern inside each term?

[glacial fern]

yes

but i cant seem to find the proper equation

i suggest that, maybe adding them all first would do me good, for eg there would be 10 x's

and 9 x^2's

[buoyant harbor]

No

Dont do that

There is a better way

Call each term a

a1 is x

a2 is x+x^2

a3 is x+x^2+x^3

And so on

[glacial fern]

so, x + a sub n-1 but i would start with 2 instead of 1?

[buoyant harbor]

What do you mean i dont understand

Recursion?

There is another way to see it

[glacial fern]

somewhat it is related to recursion

[buoyant harbor]

Express a_n with sigma notation

Can you do it?

[glacial fern]

is a_n

aₙ?

[thick raptor]

Yes

[glacial fern]

how? my calculator is dumb as hell it doesnt let me subscript numbers/variables

[thick raptor]

Calculator?

[spring thunder]

the calc won't help you

[buoyant harbor]

^

[thick raptor]

You can just write it out on paper

Or use MathBot

If you're trying to write fancy symbols

[buoyant harbor]

Latex

👀

[thick raptor]

MathJax

👀

[glacial fern]

and im dumb as hell too

E a_n?

[buoyant harbor]

a_n is basically the sum of all powers of x up to n

[thick raptor]

$$a_1=x\newline a_2=x+x^2\newline a_3=x+x^2+x^3\newline\vdots\newline a_n=~?$$

[buoyant harbor]

How would you write a general expression for a_n

[thick raptor]

Fill in the "?" using sigma notation

[glacial fern]

but my teacher didn't allow me to use terms and such

[thick raptor]

??

[spring thunder]

(we're just decomposing it for you so you see how to get there)

[buoyant harbor]

Its just to get there

[thick raptor]

wdym

[buoyant harbor]

You wont need a's in the end

[thick raptor]

That's like asking you to figure out that $$1+2+3+\dots+10=\sum_{n=1}^{10}n$$ without recognizing the nth term is n.

[glacial fern]

my teacher said that "x+(x+x^2)....+(x+......x^10)

(11n)x^n

since he said that "there would be 10 (x's)

and 9 x^2's

11-n

[thick raptor]

it doesn't make much sense, unless I'm misunderstanding what you're saying

[glacial fern]

(11-n)x^n

[buoyant harbor]

That solution isnt fun

[thick raptor]

That's another approach

oi

[buoyant harbor]

There is a more interesting one

[thick raptor]

It is fun

[buoyant harbor]

👀

[thick raptor]

This is all very fun

Don't discriminate

🔨

[buoyant harbor]

double sigma is more fun

[spring thunder]

no solucism

[thick raptor]

@glacial fern okay, then what do you get?

[glacial fern]

wdym

t-t

[thick raptor]

If the nth thing is (11-n)x^n

Like u said

Then when you sum it all up

[glacial fern]

ahh thats what i got

[thick raptor]

What do you get in sigma notation?

[glacial fern]

10x+9x^2...x^10?

n = 1 k = 10 equation = (11-n)x^n?

[thick raptor]

👍

[glacial fern]

is this 10x+9x^2...x^10 the same with this (x+(x+x^2)+.....(x+.......x^10)?

[buoyant harbor]

Yea

[glacial fern]

thank you very much!

[thick raptor]

How many x's are there?

How many x^2's?

[glacial fern]

10?

[thick raptor]

etc.

[glacial fern]

9?

thanksss

!

[thick raptor]

k

[buoyant harbor]

Double sigma...

👀

[brave void]

Okay

How would I do this one problem

Where I have a composite limit

I have lim g(f(x))

as x approaches 1

wait nvm

[viscid thistle]

um

very basic question here sorry: how would i find the function value of cot 540 degrees?

the textbook says to refer to example 4 to see how but it's about finding the functional value of quadrant angles

[patent beacon]

All trig functions have a period of 360 degrees.

== 540 - 360

Still no bot

So
cot(540) = cot(180)

[viscid thistle]

what if it was something like 450?

[patent beacon]

cot(450) = cot(450 - 360) = cot(90) = 0

[viscid thistle]

Oh.

I see. I wrote down that earlier and I got 80* as an answer and was severely confused

thanks sleep deprived brain

Thank you, I think that makes more sense to me now.

[valid vector]

How would I graph the following intervals in a single graph?
a. (-3, 4)
b. [-1, 2]
c. (-3, Positive Infinity)
d. [0, 4)
e. (Negative Infinity, 2]
f. (-1, 2) U (2, 4]

[slender river]

ok so do you know the differences between square and normal parentheses

in the context of domain i mean

[valid vector]

No, that's one thing that has me confused.

@slender river

[slender river]

ok

so square parens make the interval include the value it means to end at

[valid vector]

Oh, OK.

But how would that look in a graph? Would it simply end at that interval?

And how do the infinity signs work?

[slender river]

and round parens mean to include everything up to that specific value without actually reachng that value

[valid vector]

OK. I think I get that. And what about the Infinity values?

[slender river]

infinities are kind of hard to graph so if its like a negative infinity id just draw a line left and not put a point at all

just continue it left or whatever until you have no room

[valid vector]

OK, thanks 👍

[slender river]

so for the first one i would put circles that arent filled in at -3 and 4

and draw a line in between

[valid vector]

OK

[slender river]

(if there were square brackets the circles would be filled in)

ye

[valid vector]

Oh Ok, thanks! Got a better understanding now!

Also, would the answer to (15x^3y^2)/(25x^-2y) = (3x^5y)/5 by solving with the laws of exponents?

Is this correct?

[slender river]

yes

correct

[valid vector]

OK, thanks!

Would the correct way of factoring w^2 - 16 = 0 be by moving the -16 to the other side and then square rooting both sides of the equation? Leaving w = 4?

[spring thunder]

that's not factoring tho (and your solution is incomplete)

use the difference of squares formula

[valid vector]

Ah, you're right! So then I'd equal (a - b) = 0 and (a + b) = 0, and find both solutions, right?

[spring thunder]

yep

[valid vector]

Ah, thank you so much!

[spring thunder]

(well you can solve it your way also, just don't forget the negative sol)

[valid vector]

Lol, yeah, thing is I'm supposed to factor it, and I wasn't doing that.

[spring thunder]

mk^^

[valid vector]

Oh but wait, what would the values be for substituting a and b in the difference of squares formula if I've got w^2 - 16?

[viscid thistle]

a=w b=4

[valid vector]

👍

[valid vector]

Is this correct?

[spring thunder]

2x+1=0 <=> x=1/2

[valid vector]

Oh fuck, it's negative, right?

[spring thunder]

yea

[valid vector]

Lol, thanks, hadn't noticed that! And is the rest fine?

[spring thunder]

seems fine

=pup 8x^3+1=0

[granite stirrup]

Do more with Wolfram|Alpha pro

Query made by

@spring thunder

[spring thunder]

dem 1 sec

[valid vector]

I'm sorry what?

[spring thunder]

yeah your thing is almost correct

(for the complex sols i mean)

you didn't divide by 2 the complex parts

[valid vector]

Oh you mean the 1 +/- 2√ 3i/4 part?

Can the 2 outside the √ be divided by the 4?

[spring thunder]

yes, it should

[valid vector]

Ah OK, I wasn't sure of that. Thx for letting me know!

So it should end like this, right?

[spring thunder]

yep

[valid vector]

Ah OK, thanks!

[valid vector]

How would I simplify ^3√40x^4y^3z?

That's a cubic root, BTW

@spring thunder Can you help me?

[spring thunder]

$$\sqrt[3]{40x^4 y^3 z}$$ right?

[valid vector]

Yes that

[spring thunder]

ok so let's start with 40, what's its prime factor decomposition ? (always helpful for this kind of problems with powers)

[valid vector]

Hmm, give me a sec

Oh 4 * 10?

[spring thunder]

are 4 and 10 prime?

[valid vector]

What do you mean by prime?

Sorry for being dumb 😦

[spring thunder]

numbers that can only be divided by one and themselves

[valid vector]

Oh

OK, let me see

40 * 1?

[spring thunder]

40 isn't only divisible by 1 and 40 kek

2^3 * 5

that's the prime factor decomposition of 40

[valid vector]

Oh 8 * 5, but you can turn 8 into 2^3, I see. So then the 3 can cancel with the cubic root?

[spring thunder]

yep

so $$\sqrt[3]{40x^4 y^3 z} = 2\sqrt[3]{5x^3 x y^3 z}$$

[valid vector]

Yeah, so would the final answer be 2xy * the cubic root of 5xz?

[spring thunder]

yep

[valid vector]

Awesome thanks!

And how would I simplify this? (2 + √3)^2 - (2 - √3)^2

[spring thunder]

difference of squares

[valid vector]

This is the formula, right? a^2-b^2 = (a+b)(a-b)

The positive and negative signs are always the same?

[vernal quail]

yes

[valid vector]

Ah Ok

Wait, I got 4 as the answer to the problem. Is that correct?

[vernal quail]

Good!. That is correct ,yes.

[valid vector]

Awesome, thanks!

[vernal quail]

Anytime!

[valid vector]

Can you help me out with a couple of other problems? If you can

Like this one. I know that the x^2 cancel each other, but do the x and 8x also?

[spring thunder]

(they don't)

none of terms cancel out

there's no multiplication going on

you have to factor the numerator and the denominator first

[valid vector]

But there's division. Wouldn't the x^2 cancel each other?

[spring thunder]

then you can simplify

[valid vector]

Oh

[vernal quail]

yes they cancel out

[valid vector]

So I did this. Is it correct?

[limber bone]

y

[valid vector]

?

[limber bone]

yes

most of the time you divide polynomials this way

but if there is no common factor

then you do it by long divison

this is correct

[valid vector]

Oh OK, thanks!

For this one, do I have to factor the polynomial at the denominator at the right end?

[austere osprey]

Uh Idk what im doing

[wind igloo]

Do you know the identity of cos(2x)?

[dense zealot]

Hmm seems not

[wind igloo]

Yeah, it was double-asked too.

[dense zealot]

Lol

[acoustic matrix]

Can someone help me find the next three terms of the recursive sequence -1, 2, 5, 26?

Initial term is assumed to be -1

<@&286206848099549185> sorry for the early ping, I'm just struggling badly lol

[eternal folio]

Do you have anything else? Recursive formula, etc.?

[acoustic matrix]

sadly no...

[fading token]

it seems that each term is the square of the previous term plus one

[acoustic matrix]

my prof just provided me with those four numbers

@fading token Thank you!

[fading token]

np bro

[eternal folio]

By the way, that's not the only possible solution.

[acoustic matrix]

indeed

[eternal folio]

Afaik there are infinitely many solutions.

[acoustic matrix]

sadly yeah lol

[eternal folio]

For example, the f(x) = 3x^3 - 18x + 36x - 22 polynomial has the property that f(1) = -1, f(2) = 2, f(3) = 5, f(4) = 26; so you could take the difference of two consecutive terms and make a recursive formula using that.

[brave void]

need some help

So I got a limit

Approaching from left side

As approaching 0

|x|/x

How to evaluate?

[civic plaza]

can you graph it @brave void ?

[brave void]

okay

wait

I got it

lol

Is there anyway to solve without graphing, howevs?

[spring thunder]

what's |x| when x is negative?

[brave void]

a positive number

[spring thunder]

yes..........

for x<0, |x|=-x

[brave void]

gotcha

so it would be -1

[spring thunder]

the limit yes

[brave void]

I have another one

So I have a function

g(x)= sqrt(25-x^2)

I have to discuss continuity at an interval

Which is [-5,5]

How do I go about that?

I know if I plug in -5 or 5

Its 0

But what indicates continuity?

[spring thunder]

$$\lim_{x\to a}f(x)=f(a)$$

that's the definition of a function f being continuous at x=a

[granite stirrup]

Support the bot on Patreon: https://www.patreon.com/dxsmiley

[brave void]

k

I don't know what g(x) approaches though

It's not a limit

but a function

if it is the same at both

-5 and 5

Then it's good?

I'm confused

hello

[spring thunder]

yep it should be good

[brave void]

It has to be the same

For both values?

or a real number?

[spring thunder]

well if you want the function to be continuous at -5 and 5, you need lim_(x->-5)f(x) = f(-5) and lim_(x->5)f(x) = f(5)

but i'm doing it the very long way

x->x^2-25 is positive and continuous in [-5,5]

and the square root function is continuous for positive x

therefore by composition x->sqrt(x^2 -25) is continuous in [-5,5]

[neon vale]

Idk what to do :( I've got the points (0, 2000) and (1, 3000)???

[timber oriole]

I need help on d)

[wind igloo]

=tex f(x)=-\frac{1}{2}(x-1)^2 + 2

[viscid thistle]

can someone help me with this one

mine is the one in blue

[brave void]

Need help with limit

As limit approaches 9

x-9 / (sqrt(x) -3 )

[spring thunder]

rationalize

[brave void]

so like

root x +3?

conjugate>?

[spring thunder]

yes

[brave void]

it doesnt work

I get a bunch of junk in the numerator

over x-9

[spring thunder]

you can simplify mate

you got (x-9)(junk) over (x-9)

(if you did it correctly

[brave void]

oooh

tysm

I was multiplying unnecessarilly the numerator

[spring thunder]

kek:/

np

[brave void]

the calc itself is ez

the alg is a bitch tho

[viscid thistle]

@brave void

hey does this look right?

[brave void]

Huh?

[wind igloo]

Is the blue one f(x) and the grey one your answer? Or vice versa?

[warm nebula]

What is Pre calculus quadratic equations and factorization?

[long dew]

Last problem

Help?

<@&286206848099549185>

[elfin night]

f(x) = -4, x≤-2 so f(-2) = -4

[long dew]

How do you do that

@elfin night

[elfin night]

It tells you that on the function

Look at the top part

[long dew]

Ooooo

Lol

What about the next one

X-2

Not really an actual number

😦

[brave void]

Okay

Need help with this one

As x approaches 0

(cos(x) * tan(x))/x

[viscid thistle]

What is tan(x)?

Or what is a common identity for tan(x)

[brave void]

tan can be seen as sin/cos

[viscid thistle]

Okay

So we write

=tex \lim_{x\to 0}\dfrac{\cos (x) \cdot (\sin (x)/\cos (x)}{x}

[brave void]

yeah

[viscid thistle]

What happens here?

[brave void]

yooo

[viscid thistle]

ye boi

[brave void]

we end up with sinx/x

And thats just 1

[viscid thistle]

Noice

Kk, job done

[brave void]

tyvm

[viscid thistle]

yw

[brave void]

okay

this one I have sin^2 * x

Over x

I can pull sin out

So I have sin(sinx/x)

[viscid thistle]

Mhmm.

Then what?

[brave void]

That is sin(1)

[viscid thistle]

That isn't what sin^2 x means lel

So sin^2 x is shorthand for (sin x)^2

I hate the notation myself.

[brave void]

oh?

[viscid thistle]

But it makes your life a lot easier.

Ye

[brave void]

(sin x)^2

Over x

?

[viscid thistle]

Yep

[brave void]

so its just 1 * 1?

[viscid thistle]

Lim to 0?

[brave void]

yes

[viscid thistle]

Hmmm

=tex \sin(x) \dfrac{\sin(x)}{x}

[viscid thistle]

lim to 0

[brave void]

sin(0)

[viscid thistle]

==sin(0)

[granite stirrup]

0

[brave void]

lol

I bet

I could guess 1 or 0 for some of these

I could be 75% chance of getting it right lol on a test

These all just seem like 1,

Or 0

pi * sec * pi?

What even

[viscid thistle]

Write out the limit dude

[brave void]

I got x sec x

As x approaches pi

1 over cosign is secant

[viscid thistle]

Cosine of pi?

[brave void]

isn't that just like

-1

[viscid thistle]

Yep

[brave void]

so I got pi

over -1

• pi

[viscid thistle]

Yep

[brave void]

last one

I got as x approaches pi/4

1- tanx

over sinx - cosx

[viscid thistle]

Oh, that's a nice one actually

[brave void]

Well

I know tan is

sin/cos

1- sin/cos

over sin - cos?

that looks nasty

wait a sec

is this a complex fraction

[viscid thistle]

So what’s the distance between P and the line y=-1?

[wind igloo]

You're already in #prealg-and-algebra

Please don't double-post questions.

[stray obsidian]

so its 3 sides and 2 lengths ?

so 3h+2h?

how would i set up 17

[visual canyon]

w and l are variables i will use
2l+3w = 960
l*w = trying to max
2l = 960-3w
l = 480-3/2w
(480-3/2w)w
-3/2w^2+480w
you know -b/2a would give you the w value that you need to be max
so -480/-3 = w= 160
so w=160 and then l is 2l= 980-480 l=240 @stray obsidian

my bad a little late lol

[stray obsidian]

thank you

[stray carbon]

Anyone good at pre calculus in this channel?

[wind igloo]

[steady token]

well this is? related to math but how can you really pass precal tests, ive been so stressed lately because honors precal is going so fast for me

the material is being covered so fast f

[jagged gazelle]

F what are you on currently?

[steady token]

im on composite functions

normal precal wouldve covered this in like 1 week

1 week later*

[jagged gazelle]

what's about it that you dont get? i think smth that can help is like, color coding them

[steady token]

well not composite functions specifically

everything ive learned is so fuzzy in my head

like i read my notes over and over

just doesnt stick

[jagged gazelle]

uuhh a big thing in pre calc i did was just write every step to solving it down and also i really got familiar w the calculator and stuff

[steady token]

write every step to solve?

[jagged gazelle]

as in, before pre calc i used to jump ahead and not show little bits of work sometimes but now ill show every little thing because it gets way easier to see my mistakes

[steady token]

maybe its just me, last year in algebra i was horrible at trig

oh

i have no idea why im so bad at trig, i was getting a+s the first semester

then when trig was being covered in the second semester it went to an a-

now in precal im at a c

almost d

[jagged gazelle]

i feel precalc gets easier later on, or at least easier than trig for me

[steady token]

ill try your trick in my next test

i hope so lol

its still the beginning of the year

but it doesnt justify the fact that im getting an c- while my peers are at a+s

[jagged gazelle]

don't overthink it and just take each problem a step at a time and take your time w your work

[steady token]

yeah ill try

thanks for the advice

just an shock to me ive always been getting good grades, never handled this much stress before. Probably seems like such a small problem lol

[jagged gazelle]

np, i dont think composite functions should be hard if you take it slow and write it out (unless you have trouble with like...the actual calculation stuff) -- ahh yeah i getcha,

i'd keep a reference table for pre calc of little tricks and formulas

[steady token]

well its not exactly composite functions

i completely failed difference quotient part of my last test

[jagged gazelle]

wym?

oh

[steady token]

also the graphing part

[jagged gazelle]

uuhhh iirc i just used the fucken...triangle shit for the difference quotient stuff

have u ever seen people find slope via a right triangle? its way easier to remember imo

[steady token]

hmm okay

i guess even more practice is the way out of this mess then

i should honestly just get a tutor

[jagged gazelle]

and eitheir way my point about taking it slow and color coding still applies to difference quotient shit. its just a lot to look at bro

@steady token look at this

[steady token]

that relates to the difference quotient

??