precalculus

[frigid trout]

Ohh you’re right

Thank you Saul

[viscid thistle]

Is there a way to factor this by hand or by calculator this is the only part i keep getting confused on for inequalities with polynomial functions and its really really pissing me off cause i could solve it online but i don't know how to do it by hand or by my own doing

[warped cipher]

GCF

[normal coral]

#calculus

[normal coral]

you are in the pre calc channel

pre calc

#calculus

[gaunt sand]

Take out the x

And factorise it

x^2(x-4)

[viscid thistle]

I still just don't understand lol for the squared part at least

What happens to the x³

[gaunt sand]

wym what happems

to it

if u expand, u do x^2 * x

and x is just x^1

so x^2*x^1 = x^2+1 = x^3

indices rule ^

[viscid thistle]

Watched a vid and reread comment it makes a lot more sense now thanks 👍

[marsh condor]

U want help?

[jaunty crow]

Well the homework was already due

But I didn't understand it

So id appreciate the help

[marsh condor]

Factor then take the roots then test a number in between and then just use multiplicity for the other intervals

Do u know how to calculate the derivative?

[jaunty crow]

Yea

[marsh condor]

Okay that’s the bulk of the problem

A horizontal line has a slope of 0

Therefore f’(x) = 0

Then you must solve for x

9e^x(sin(x)+cos(x)) = 0

When do sin and cos have + and - outputs

2nd and third quadrant

But the domain is 0 to pi

So only second quadrant

In the second quadrant they have the same |output| at 3pi/4

So that’s that

Then u have to plug that value into the original problem

To find the y value of f(x)

I assume ur allowed to use a calculator

[marsh condor]

Also note that 9e^x can not = 0 so that factor is discarded

[jaunty crow]

We're not

[jaunty crow]

Yea thts wht I thought but I didn't know how to solve for x when sinx+cosx

[marsh condor]

Sin and cos have - and + values in the 2nd and 4th quadrants

[jaunty crow]

Yea

[marsh condor]

They’re equal -cos(x) = sin(x)

At 3pi/4

[jaunty crow]

Oh

Yea

Makes sense

Thnx

[warped cipher]

? what

[warped cipher]

you start with greatest common factor and it then it gives you x(x^2-4)

x^2-4 has a perfect square

[marsh condor]

what?

It’s factorable but it isn’t a perfect square

(x-4)(x+4)

Subtraction of squares rather

[warped cipher]

meant it has a perfect square in factorable not just only a perfect square

whats the difference anyway

[marsh condor]

The two terms r perfect squares

Technical stuff lol

[warped cipher]

some people still call it a perfect square in factorable lol

[warped cipher]

I get it's that don't think I don't know about that

try khan academy if you haven't

[warped cipher]

apply l'hospital's rule

[scarlet vine]

i so regret not studying precalculus before getting into cal AB bruh

[scarlet vine]

hmmm

i would prefer to use either the factoring method or rationalization instead of that ;-;

im not really sure why tho

[pine geyser]

do you still need help with this?

[warped cipher]

applying the l'hospital's rule will faster than that

0/0

[normal coral]

this is precalc so most people in here wont really understand/be fluent in l'hopital since that is usually taught in calc 1

[warped cipher]

l'hopital rule is taught in precalc wdym

[normal coral]

can’t tell if ur being sarcastic or it’s actually taught in pre calc somewhere

cause most places I have seen, it is taught in calc 1

[warped cipher]

it depends which country honestly

but I get calc 1 taught in high school

[normal coral]

ah ok

[warped cipher]

not really actually calc but they teach l'hospital rule at least

[scarlet vine]

:))

actually

i havent learned about that rule

but i know the form tho

[wanton marsh]

Any one that would be willing to tutor? Can pay for time spent of course.

[dawn osprey]

What do you need help with?

[faint igloo]

Paying for tutoring is against server rules, but there are plenty of people here willing to help for free

[slim steppe]

You've also got online resources to use for FREE

[wanton marsh]

Ah, my apologies. @faint igloo

[long tulip]

<@&286206848099549185>

[hushed loom]

Did this help?

[lean nest]

both of these are because fractions exist

[frozen dirge]

" if there is a limit find it "

[dawn osprey]

Well, from either side (negative or positive) we are approaching some value at x =1

[frozen dirge]

ye

[dawn osprey]

you'll be infinitely close to x =1 which should result in y =(?)

[frozen dirge]

0 ?

or infinit

[dawn osprey]

maybe that wasn't a good way of explaining it, think of it like this...

what value is the function approaching if we plug in x =1?

[frozen dirge]

4

like according to the equation

is there a method to do this

im not asking for the straight up answer but i wanna know how its done

im a visual learner

1^2 + 3 = 4 right

[dawn osprey]

Right, the limit value of a function does not depend on how the function is defined at the point being approach (whether or not its not part of the graph)

[frozen dirge]

so 4 ?

ight

[dawn osprey]

right

[frozen dirge]

also can u stay here

i got a few more questions

[dawn osprey]

You can ask them

I might not be able to answer them tho, I gotta go soon

[frozen dirge]

bet its just this 1 question

[frozen dirge]

sorry its that way

[dawn osprey]

okay, what about this question

I won't just do your hw if thats what you're getting at 😭

[frozen dirge]

im tryna ask what it is

not the answer

im tryna understand

its that if the value of the given quantity exists and if it does find it

that

[dawn osprey]

yea, so limits are asking what value is being approached, they differ from per say f(0) in that f(0) is asking the defined value

so in this case f(0)= 4

but the limit as x approaches 0 will be different ( depending on what side you're coming from)

If that didn't answer your question, try watching a video like https://youtu.be/7Q2HwTHcxA0?si=XAyux28wp_nBvCkG and see if that helps explain

I gotta go for now tho, hope you can get it sorted out

[frozen dirge]

i seen this bru

[thorn creek]

that looks more like a chart for a sportsball play than it does a math problem

[dawn osprey]

If you’re asking how to answer the question from what I can tell it would be:

If (e) is undefined, explain why it has no value. In this case it’s because there was a removeable discontinuity

[thorn creek]

in that example f is undefined at 2 because it's simply not defined at 2

[dawn osprey]

Yea

[thorn creek]

whether a function has a limit at x has nothing to do with whether it's defined at x

it has to be defined on a deleted neighborhood of x, but not necessarily at x itself

and in this case f is defined on a deleted neighborhood of 2

[dawn osprey]

Yea, maybe removable discontinuity wasn’t the right word, but I don’t think he really has a grasp of what lim x->n is asking

[thorn creek]

no, you're right, it is a removable discontinuity

the key takeaway from that exercise is the understanding that the limit of f at x has nothing to do with what f does at x itself, only on what f does near x

[dawn osprey]

Yea that’s what I was trying to say with the “a limit is the value being approached”

[thorn creek]

the function f(x) = { 1 if x is an integer, 0 otherwise } has limit 0 at every real number

[dawn osprey]

My bad I thought you were saying something else

[thorn creek]

and is discontinuous at every integer and continuous everywhere else

[whole island]

figure out what the hole is at 1 (for reason why $x\neq 1$).

plug in 1 for x^2+3 and your answer is the limit as x approaches 1 (from both sides) of f(x) goes to 4.

$x \neq 1$

[frozen dirge]

hole means discontinuity right ?

[obsidian monolith]

Tank_Driver011

[whole island]

The function is discontinuous -- do you know which type of discontinuity it is?

[frozen dirge]

no

[whole island]

we have removable, infinite, and jump.

[frozen dirge]

oh yea i know jump

must be removable then

[whole island]

removable - there is a hole
infinite - vertical asymptote
Jump - a split in the graph

[frozen dirge]

whats an asymptote

so its jump

coz its a split

a long split tho

[whole island]

no, sorry. jump looks like this (the thumbnail of the video)

an asymptote is a line that the graph never touches.

[frozen dirge]

ah bet

dude its a jump

the picture if just tiltied 90*

[whole island]

this image?

[frozen dirge]

no no

[frozen dirge]

this image

i already found that one!

[whole island]

oh, i'm talking about this.

[brittle ice]

the notion "getting closer and closer" can be made precise using convergent sequences

[whole island]

oh!!!

[frozen dirge]

oh bet

ye i see what ur saying

[whole island]

,rotate

[obsidian monolith]

Couldn't find an attached image in the last 10 messages.

Sep 26, 2023, 2:15 AM

[whole island]

,rotate 90

[obsidian monolith]

Couldn't find an attached image in the last 10 messages.

Sep 26, 2023, 2:15 AM

[frozen dirge]

hol on

[obsidian monolith]

Tank_Driver011
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[frozen dirge]

,rotate

[whole island]

25 or 26? Both? let me explain 25 and you complete 26.

a. f(1) - you plug in 1 for x and look for y (look at the graph at x = 1, notice it is a hole/DOES NOT EXIST, therefore, the point that is circled in is the answer at (1,2)

b. limit as x approaches 1 for the function f(x): approach x=1 (on graph) from the left and the right, notice how the graph splits (from the left, you are above the right piece of the graph). Since the right and left do not give the same answer (right gives (1,1) and left gives (1,3), then the limit as x approaches 1 DOES NOT EXIST.

c. plug in f(4), find the point on the graph -- it has a hole at this point so it is DNE

d. limit as x approaches 4 for the graph f(x) meets at the same point (both left and right), it is continuous, therefore as x approaches 4, f(x) approaches 2.

REMEMBER
f(a) is different from limit x --> a f(x) -- the limit approaches some value, f(a) is that point and if it has a hole for f(a) then it does not exist but if hole is for limit, you write the value it approaches. see above for explanation

@frozen dirge

[frozen dirge]

wait

im eating rn ill look into it

thanks!!

[rain palm]

I'm struggling on this question could someone please explain? I tried my best on the answers

[floral horizon]

guys, im just starting limits, was wondering if someone could answer this cus i havent read it yet. Whats a derivitive in definition? WHats a limit? if someone could ping me or reply thatd be cool, its been a childhood question of mine.

[viscid thistle]

Can |x| <_ -4 be represented using a number line?

can anyone help me factor this i dont know whrere to begin lol

[gaunt glen]

(x-2)(2x^2 + 7x+3)

[lapis ravine]

hii, new to the server i have a question...
is the coordinate of the focus of a parabola that opens to the left (a, 0) or (-a, 0)?

[dim goblet]

(-a,0 ) for parabola y^2 = -4ax

[viscid thistle]

can anyone solve this polynomial inequality I know how to do everything im just confused on the answer

[sour bolt]

solution is (-1,5). You have only one point hear

[distant ledge]

a) False because you still have d
b) True because d cannot divide by (x-c)
c) True because c-c in factor x-c can make zero in (x-a)(x-b)(x-c) so d left
d) False because d cannot divide by x-a to get some d

[digital mirage]

can u guys suggest me any video to learn Riemann Integra in depth ?

[west citrus]

https://www.youtube.com/watch?v=842rgQP_OgI&list=PLBh2i93oe2quABbNq4I_-hyjhW8eOdgrO

[tepid escarp]

Hi guys, our teacher wants us to make a 3D model of all the conic sections. Any ideas or suggestions?

[hushed sphinx]

Sounds like a cool project. I think I'd try to make it work with office paper for the cone and stiffer cardboard for the plane that intersects it.

[thorn creek]

i was thiunking 3d printer, but yeah that's probably less work

[digital mirage]

in 1 one both end points are not meeting , but in 2 both end pints are meeting , how is this possible , in 2 one for one value of x how two values of y are possible ?

[stark nova]

https://media.discordapp.net/attachments/1156486660742189066/1156486660901580900/image.png?ex=651525a2&is=6513d422&hm=109cc31d6173d06ca4e1f66d9c260e2302f437989ea21ab6c3e1f18c8803df8a&=&width=1440&height=392

f(x) = (x-2)(x-3)

im going crazy i have tried breaking it and removing the roots but nothing

its hs math and i havent done derivatives yet so please no derivatives

[trim cape]

try multiplying by the conjugate

[stark nova]

thats what i tried but it doesnt bring anything useful

i know thats the only way to solve it but im kind of stuck

[trim cape]

what did you multiply it by

[stark nova]

i broke the 2 and multiplied the one by /x+6 and the other with /x+1 -1

so its x+6 -x with the denominator being differnet of course

and from then on i tried making it x-3 +9 and getting rid of the x-3

but it doesnt really work

[trim cape]

can you send a picture?

[stark nova]

wait i need to write it because i got rid of the other

1 minute

[trim cape]

ah you split it up

[stark nova]

yeah

[trim cape]

i wouldn’t do that

[stark nova]

but if i do it without splitting it it will end up with a /x+6 * /x+1

and i cant remove it unless i break it again

[west citrus]

Only one endpoint in 2

[trim cape]

look at the numerator as /(x+6)-(1+/(x+1))

then you can multiply by the conjugate

[stark nova]

then i will end up with /x+1

you mean to then split and get rid of it or

[trim cape]

no dont split

[stark nova]

wait ill try it

without splitting

ok

so now its 2x -2/x+1

should i do congujate agian

[trim cape]

uhh the 2x should be a 4

[stark nova]

but isnt it x+6 -(1+/x+1)^2

[trim cape]

yes

[stark nova]

so its x+6 -1 -2/x+1 + x +1

so -1 and 1 goes away and

oh the 6

ok ok

[trim cape]

distribute the minus to all terms

its -x-1 at the end

[stark nova]

am i an idiot?

yes

ok so its -2 -2/x+1 right

[trim cape]

you forgot the 6

[stark nova]

-4 -2/x+1

so do i congujate again

[trim cape]

Well its +4

[stark nova]

thats true

[trim cape]

And then yes

[stark nova]

oh oh oh

I want to give you a kiss

but thanks

yeah now it comes out

[trim cape]

no problem

[void mesa]

Why is thins wrong?

[digital mirage]

but it is showing two end point in 2...

[pine geyser]

is this answer wrong?, i dont really think thats incorrect

[void mesa]

it's wrong because it's actually a floor function

stupid ass website didn't display it properly lmao

thought it was a absolute value notation

[magic geode]

"with vertex at (5,4) and focus at (5,-1)" how do i find the properties? C, V, F, D, A, LR, 1/2 LR, L, R?

[pine geyser]

oh ok lol

[void mesa]

@pine geyser https://youtu.be/q68Hl7DhsuQ

[void mesa]

yea it is about this

[last root]

Why this integration = -1?

[west citrus]

Take the primitive and do the value in 1 - the limit in 0

Cauchy integral definition of integral

[pine geyser]

I got it, thanks

[calm fractal]

anyone know what these notations mean

or symbols rather

nvm simple google search explained it for me

[wicked knot]

i need help with this thanks so much in advance <33

[strange perch]

yo i need help in my pre calc class

plz add me if you can

[wooden brook]

$$I_{n} = ∫(x^{2} + 1)^{-n} dx$$

Show that

$$I_{n+1} = \frac{x(x^2 + 1)^{-n}}{2n} + \frac{I_{n}(2n-1)}{2n}$$

[obsidian monolith]

KnightOnF1 ♘

[wooden brook]

Reduction formula

But how

[iron spoke]

$\sqrt{(2^n+3^n+4^n)}$

[obsidian monolith]

xxOctavianxx

[willow bear]

that's an expression

what are you asked to do with it

[iron spoke]

find n

[willow bear]

this is not an equation

you cannot solve for n

!original

[tender quest]

Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.

If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.

[mint forge]

Olympic math?

This is the precalculus channel

[iron spoke]

uh

maybe

[iron spoke]

sorry, prove that the expression is rational

[mint forge]

I think that it can be rationalized. I'll dm you later

[iron spoke]

please do that, thank you so much!

[willow bear]

are you sure that's what it says

because to me it looks like "determine those n in N for which the expression is rational"

[iron spoke]

that's right

my bad

[thorn creek]

whee number theory

there's a well-known proof that 2^n + 3^n is never a perfect square, so i suspect a similar strategy to that in that well-known proof would work

https://math.stackexchange.com/questions/1794072/prove-that-2n3n-is-never-a-perfect-square

[onyx lotus]

i have a question why doesnt the 3x get cancled out?

[summer ruin]

because it's a typo

[gray maple]

What up mathletes

[normal compass]

yo am struggling with functions and two-dimensional coordinates, internet doesn't give much better explanation, i think y'all students can help me (?)

[iron spoke]

Did you find anyhting?

[willow bear]

no and i did not really care much about this problem in the first place

[iron spoke]

i see

well that sucks

[empty trellis]

Can anybody help me with a question? I asked ChatGPT this question and told me that all values of k work.

If the function f is defind by f(x) = 2x + k and the function g is defind by g(x) = (x-5)/2, for what value of k is f(g(x)) =g(f(x))?

[twilit quartz]

2x + k?

@empty trellis

[empty trellis]

yes

[twilit quartz]

@empty trellis i think its + 5

for k

[empty trellis]

can u explain plz

🙏

[twilit quartz]

Sorry if i dont explain this well, im still learning functions myself. So i just placed a guess, and put 5, and tested if it would be true, and wrote it down.

g(x) at 10, would be 2.5, and 2.5 at f(x), would be 10, and then i did it again

f(x) at 10 would be 25, and 25 at g(x), would be 10

both answers come out to 10,

the = 10 in the picture isnt the answer for the functions btw, its for the functions below i just wrote them there

[empty trellis]

Tysm

[timid agate]

why won’t this work?

[slim steppe]

Get rid of y=

[timid agate]

still doesn’t work

desmos says «Integration bounds can’t depend on the integration variable ‘x’»

but it works with y

[slim steppe]

Desmos only calculates the definite integral with numerical bounds

Doesn't calculate some integral that has variables as bounds

@timid agate ^^^^^^

[thorn creek]

desmos is right, the variable of integration cannot be a bound of the integration

[thorn creek]

untrue:

you can get pretty complcated, too:

the issue is that you can't have the same variable in the bounds as the variable of integration because it's ambiguous what you mean

[warped cipher]

bro is too good

[slim steppe]

But that doesn't tell me anything other than the anti-derivative of that exponential

It doesn't fully compute the anti-derivative function for me

Just shows me what it is

[thorn creek]

yeah, i didn't ask it to do that

but that wasn't the point i was trying to make; the claim was that desmos couldn't graph curves defined by a integral having a variable bound, and that's not true

[cursive crag]

my fellow precalc students

what is up

[short saffron]

Suppose there is a function $y(x)$ satisfying $\frac1{1-x}\le y(x)\le \tan(\frac{\pi}{4}+x)$. For which $x$ is this function bounded?

[obsidian monolith]

sunside

sunside

[short saffron]

Never mind my question.

[strange perch]

who got the answers

[frigid trout]

solve for x

move 3 on other side and divided by -3 to get x by itself

then you flip the sign since youre dividing by a neg

-3x < -3

= x > 1

so x values have to be greater than 1 and they cant be one so open circle facing right if im not mistaken

[hexed apex]

can someone help me with this

[summer ruin]

properties of logarithms

[restive berry]

wait i was working with this sort of stuff just a few hours ago

lol

but i see someone else has already answered

[jagged vine]

hey I just wanted to know if im doing this right or not bc I have been trying to teach myself diff ways but I got 2 diff answers

i got f^-1(x)=7/3x+1/3

but tried a diff way n got f^-1(x)=3/7(x-1)

[thorn creek]

i have no idae what proper inverse function notation is

[thorn creek]

i get 7/(3x)-1/3 so you may have made a mistake somewhere

[jagged vine]

i just dont understand proper inverse function notation

[thorn creek]

i don't know what that means

it's something your textbook or your instructor has defined, it has no standard meaning of which i am aware

if i do the "replace f(x) with y, interchange y and x, and then solve for y" i get "y = (-1/3)*(x-7)/x"

you then replace y with f^-1(x)

using a computer algebra system: ```
sage: solve([y==7/(3x+1)], x)[0].subs([x==y,y==x])
y == -1/3(x - 7)/x

[hexed apex]

can someone help me with b)? i dont know how to do it

[thorn creek]

i don't like that question. a vertical asymptote is not merely a point at which the function is undefined because it involves a division by zero

take the function f(x) = { 0 if x is an integer, 1 otherwise }

1/f(x) is { 1 if x is not a integer, undefined otherwise }

i would not consider 1/f(x) to have a "vertical asymptote" at each integer even though 1/f(x) is undefined at each integer because the definition involves a division by 0 at each integer. for x to be vertical asymptote, the function should approach infinity on a deleted neighborhood of x, but 1/f(x) is bounded on every (sufficiently small) deleted neighboorhood of any given integer

however, you'll have to review the definition of "vertical asymptote" that your text or instructor has given you and apply that definition, which might not agree with my sense of how that term should be defined

[jagged vine]

anybody have a site that can do this? mine just wont give a maximum lol

[thorn creek]

desmos may provide insight here

[proper barn]

hey, im a precalc honors student in unit 2 rn. the first unit was the unit circle, and i completed all quizzes and tests with relatively good scores. onto unit 2, i unfortunately missed many days due to unforeseen circumstances, and am really behind and need help learning the content. i have a quiz on monday, and the unit test on tuesday. the unit is called graphing trig functions, and we are not allowed to use any form of calculator under any circumstances. if someone can devote some time to helping me learn this unit, that would be really helpful

[viscid thistle]

can anyone find a video on where i can learn about this i just don't understand ;/

[gaunt sand]

Which part are u struggling with

Maybe someone here can assist

[viscid thistle]

I found out how to do it dw thank u tho

although if anyone can can someone check one of my problems for work its x int

[viscid thistle]

curious if its -4 or none

[lunar viper]

how would i do this?

[junior heart]

Nobody in my class can solve this, so now I'm trying to get help elsewhere. The answer list says a cubic function with negative a-value, with local maximum at x=4 and local minimum at x=-2, if it is to any help:

A function which is valid with the restrictions given below:

[thorn creek]

those are some big parentheses

[glad nova]

hey guys, I was wondering if anyone had some good resources for calc stuff?

[hexed apex]

is this right? i know that at x=7, the slope is 0 and idk whether i should include that point

[summer ruin]

f'(x) = 0 is not f'(x) > 0

[hexed apex]

yes i know

[summer ruin]

what's the problem then

[hexed apex]

for example, for 5 < x < 7, 7 is the endpoint of the interval and since its the > and not the ≥, i am wondering if its correct to select that as the answer for f'(x) > 0 since the 7 is not included in the interval but just stops there right?

or am i wrong

[summer ruin]

it is correct

you should check your other answers though

[near viper]

help!

how tdo i solve

[tall lion]

p=2/5 ?

[viral mesa]

[wheat radish]

P=1

[novel spear]

make a least common denominator so
(6(p-3)+p*(p+3))/(p+3) * (p-3)

distribute
6p-18+p^2+3 / (p+3) * (p-3)

combine like terms
9p-18+p^2 / (p+3) * (p-3)

multiple sides by denominator
9p-18+p^2 = (p+3) * (p-3)

simplify right side
9p-18+p^2 = p^2-9

subtract p^2 from both sides
9p-18=-9

add 18 to both sides
9p = 9

divide both sides by nine
p = 1

[viscid thistle]

divide acosx-bsinx/bcosx+asinx by bcosx in both numerator and denominator

[native steppe]

is 7*1/3x+1

[warped cipher]

thank you chatgpt

[hoary leaf]

help can someone explain how it's C (I made an equation g(x)-1/2f(2x) but the values i plug in don't work)

[radiant kite]

help

[novel spear]

bruh

i typed that shit

[warped cipher]

!nosols

[tender quest]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[novel spear]

@warped cipher what does !nosols mean

[warped cipher]

read it

[novel spear]

no solutions

crazy

[warped cipher]

it's shortcut for no solutions or answers I think

it's against the rules

[novel spear]

interesting

why’s it against the rules

[warped cipher]

idk tbh

but it could many people just want others to do their hw without understanding how they did it or some of them just wanna cheat during the quizzes/tests without understanding it as well

[novel spear]

well mb i didn’t know

[exotic void]

hello can anyone explain why this is wrong

[thorn creek]

the first one is marked wrong because you omitted a repeated root

and in the second one you only gave one of the three real roots, the polynomial has two other real roots

[viscid thistle]

where are you getting stuck

what are you doing to solve it

[sweet agate]

got it

[restive dome]

does anyone have a trick for solving rational functions with absolute values?

[radiant kite]

turn the rhs into sin(tan^-1x)

then eventually i get tan^-1(x+1)=tan^-1x

which gives no solution

[faint anchor]

I need some clarification about inequalities. If I have the following inequality:

1/2 * X <= Y <= 2 * X
Am I allowed to look at the upper bound and lower bound individually and produce bounds for X? Like so:
1/2 * X <= Y gives X <= 2 * Y
and
1/2 * Y <= X
So we conclude that X can not be bigger than 2 * Y or smaller than 1/2 * Y?
Thanks

[sweet agate]

??

[plush sparrow]

yes you can, using algebra which you have done correctly :D

[acoustic heron]

yo how can i do hyperbolas my prof didn't teach us how but having a midterm tomorrow

[warped cipher]

isn't that a reciprocal function graph?

[acoustic heron]

i think it prolly is?

[warped cipher]

\sethlcolor{Orchid}
\subsection*{$\bigstar$ Reciprocal Function: $f(x) = \frac{1}{x}$}
\begin{minipage}{0.5\textwidth}
\begin{tikzpicture}
    \begin{axis}[
        grid=both,
        axis lines=middle,
        xmin=-3, xmax=3,
        ymin=-2, ymax=2,
        xlabel={$x$},
        ylabel={$y$},
        ]
        \addplot[RoyalPurple, thick, domain=-3:-0.1] {1/x};
        \addplot[RoyalPurple, thick, domain=0.1:3] {1/x};
    \end{axis}
\end{tikzpicture}
\end{minipage}
\hspace{1cm}
\begin{minipage}{0.4\textwidth}
\centering
\begin{tabular}{cc}

$x$ & $f(x)$ \\

-3 & -0.33 \\
-2 & -0.5 \\
-1 & -1 \\
1 & 1 \\
2 & 0.5 \\
3 & 0.33 \\
\end{tabular}
\end{minipage}
The reciprocal function $f(x) = \frac{1}{x}$ has \hl{two hyperbolas} in the 1st and 3rd quadrants. As $x$ approaches 0 from either side, $f(x)$ approaches $\pm\infty$.

[obsidian monolith]

Akira 🍉

[warped cipher]

this you want?

[acoustic heron]

nope this is the one im talking about

only horizontal and vertical

[warped cipher]

can't tell if this is absolute value or parabola

nah that's looks like reciprocal function

[viscid thistle]

hyperbolas?

is mathematical induction helpful in calclus or pre-calc?

generally no

[viscid thistle]

but you should learn it anyway

[viscid thistle]

i see, but where do we generally use it? in what branch of mathematics?

just curious

[viscid thistle]

if you're studying calculus in a formal way, like analysis, you use proofs to prove a lot of statements and such

[viscid thistle]

Thank you for the explanation

don't worry about proving anything if it's your first time learning calculus

just build intuition

[viscid thistle]

You mean proving the limits problems?(just an example)

[viscid thistle]

no, more things like theorems. The fundamental theorem of calculus, for instance

mean value theorem

i see, but i do have a question, why do we use continuties? and what is the right way to do them?

can anyone help with this

[viscid thistle]

continuity is important in calculus

if a curve is discontinuous, you may not be able to apply certain tools

limits are used to determined continuity at a certain point

[viscid thistle]

after fn,ITF,lim

[warped cipher]

#calculus

[misty saffron]

nice

[soft copper]

can anyone help me with the letter c

[viscid thistle]

lets say that
there are two concentric squares where the bigger one has a side of S and smaller one has side of S-1,
The shaded area clearly corresponds with the function A(S-1) as the shaded area tends to show the smaller square
Similarly the sum of the area of of the unshaded region and shaded region corresponds with the function A(S)

so with the shaded area A(S-1) will correspond

the other expression i think corresponds to the sum of the unshaded regions

@soft copper i suppose this must be oyur answer

[woeful jungle]

nice

[soft copper]

ty

[digital garnet]

How do you find the phase shift?

[paper hearth]

Any of you guys wana help my dumass pass the class?

im honestly confused on some stuff some explaining might help

https://tenor.com/view/champagne-barbie-cookie-monster-gif-3214247160537358779

[potent willow]

i can help!(i cant i didnt learn anything from precalc)

[warped ridge]

Did you solve it yet

[exotic void]

Can someone explain how (x-4)^2 +1 is facted to (x-4+i)(x-4-i)

[vapid plaza]

+1 can be written as -i^2

[exotic void]

then why is it +i and then -i?

[summer ruin]

a^2 - b^2 = (a-b)(a+b)

[exotic void]

oh

i think it's clicking

thank you

[digital garnet]

yes I did

[warped ridge]

Aight

[nova cargo]

no i think that A(S)-1 would be S^2 - 1, which would correspond to the difference of two squares, meaning that A(S)-1 is everything except the smallest square

[viscid thistle]

im not sure but yeah this was my approach

[twilit quartz]

#help-23 sorry guys, but nobody is responding, if u wanna look at this, tyvm

[thorny heart]

can anyone teach me basic integation and special integrals?

[slim steppe]

Use online resources. Better than we can explain it for you

[warped ridge]

!~noadverts

[thorny heart]

where can i find them (apart from yt)

[slim steppe]

There's khan Academy, Albert.io, and youtube has videos of university lectures that you can watch

[quartz leaf]

hi i had a question about chain and product rule

like say you had a problem

is there any scenario where you could use product or chain rule to differentiate it and get the same answer?

[stark stream]

i'm assuming u are talking about a question like (2x-3)^2

in this case you can probably use both and get the same answer

chain rule will give you 4(2x-3)

and so will product

[golden frost]

How do I figure out the values on the sides and how their placed

[willow bear]

do you still need help with this?

[sick trail]

hey how do i differentiate x^3+4/x

where do i start

[inner cobalt]

um

[inner cobalt]

you split the differentiation

d/dx of x^3 + d/dx of 4/x

[rain marten]

yeah

[inner cobalt]

then

[rain marten]

then 4/x is rewritten as 4x^-1 through index laws

[inner cobalt]

power law it

[rain marten]

yeah

[inner cobalt]

yas

[rain marten]

d/dx (x^n) = nx^(n-1)

anyway i came to this channel so i could ask a different question, maybe its a bit too advanced for this channel but im putting it here because im not at university yet idk

i was thinking about factor theorem and how if f(n) = 0 then (x-n) is a factor of f

[inner cobalt]

o

[rain marten]

& maybe that rule only applies to polynomials but i thought "what about sin"

[inner cobalt]

sin

[rain marten]

yeah

this is where it gets wacky

[inner cobalt]

wat fnction

[rain marten]

because sin(0) = 0 so that implies that x is a factor of sin(x) right?

but then there's also sin(pi) and sin(2pi) and so on

[inner cobalt]

yeah

but

graphically

sin isnt the same as a polynomial

so you cant really

classify it that way

and u cant really factorise it as well

[rain marten]

so does that suggest that sin(x) is an infinite product of (x-0pi)(x-pi)(x-2pi) and so on??

[inner cobalt]

it could be

[rain marten]

but then you can think about maclaurin series & then suddenly it is a polynomial

[inner cobalt]

oh yeah

i forgot about maclaurin series it turns the sin into

well yeah

[rain marten]

except that would get way too big & you would have to scale it down so that the maxima and minima are at 1 and -1

[inner cobalt]

that was what i was thinking

cause

[rain marten]

so what do you scale it down by? infinity? since its infinitely big polynomial

[inner cobalt]

isnt it only regarding the x value

s

[rain marten]

wdym

[inner cobalt]

if the amplitude

wait

[rain marten]

ill get desmos to show it

[inner cobalt]

the first function

[rain marten]

the red polynomial is wayyyyy too big but if you scale it down by like 1000 it kinda looks like sin a bit

[inner cobalt]

just the roots of the equation

sin(x)

[rain marten]

thats another problem also because the max min points arent all the same

[inner cobalt]

yeah

cause its a polynomial

[rain marten]

like is that a problem that just solves itself as you add more terms or

idk

[inner cobalt]

i thougth about that

since the degree of x is increasing each time

[rain marten]

heres more terms scaled down more

[inner cobalt]

close

[rain marten]

you can see it stays closer for longer

[inner cobalt]

i feel like it would be an approximate not

exactly

but i couldnt be sure

[rain marten]

so if you have loads of terms like infinitely many of them would it just be sinx eventually

idk if im just spouting nonsense here im quite ill

[inner cobalt]

not sure bout that

since a polynomial term has finite number of terms

and the sinx function has infinite number of roots

im afraid sinx cant be expressed as a polynomial

not possible BUT

a sequence may work

they are periodic

[rain marten]

i mean maclaurin series is a proper thing that has been properly proven

so you're just wrong there

because its an infinitely long polynomial it can have infinite number of roots

and thats what im thinking about also

[atomic goblet]

Anyone that’s good at trig

I need help on this one question

[tough veldt]

I have an incoming exam of a math course two weeks till now, The course is about differentiation: rate of change, function of a function, implicit function to differentiation of trigonometric and inverse trig function. I don't know this math course. I want to ask for help if anyone has a simplified documentation for this and Youtube channels suggestions that explain the concept. Please, it will be a great help for me.

[river hearth]

check out 3b1b's videos on the essence of calculus (theres like 12 u probably dont need to see them all)
https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

[tough veldt]

Thanks for your help. Really appreciate it

[radiant kite]

,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!

[radiant kite]

,list

[obsidian monolith]

My commands!

Use ,ls to obtain a briefer listing, and use ,help <cmd>to view detailed help for a particular command, or ,help to view general help.

If you still have questions, talk to our friendly support team here.

Meta

View or set meta-information about me.
​ ​ ​ ​ ping: Check heartbeat and API latency.
​ ​ ​ ​ help: Bot and command usage information.
​ ​ ​ ​ list: Lists all my commands!
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Page 4/4

[sick trail]

how would one work out question 5a

and question 6

[zinc fulcrum]

bro what

[vapid plaza]

Bro is writing hieroglyphics

[willow bear]

what the fuck does this mean

[mint forge]

<@&268886789983436800> sorry for tags

How much raid in this server

[solar olive]

they absolutely can

well

an infinite product

[inner cobalt]

Ya

Which isn’t

[solar olive]

okay, u could argue about its taylor series being a polynomial representation of it

[willow bear]

what is infinity minus 1

where did you see this

photo?

[delicate shore]

Guys help me solve this im stuck on a step

This is differentiation byw

[hushed sphinx]

Doesn't look like precalculus.

[dense mango]

can someone PLEASE show me the steps of differentiating this??

[hushed sphinx]

Doesn't look like precalculus either.

[dense mango]

so what is it

calculus?

[hushed sphinx]

Yes.

[dense mango]

ok I'll change channels then

[frosty laurel]

yall am abt the rip my brains out rn

can someone help me solve this

oh nvm this is preclc

[slim steppe]

You can re write -x/2 as -1/2 times x

Then just use u sub if you'd like

[frosty laurel]

ty bri

broo

😭

[frosty laurel]

thta exactly whqt i did

[fiery sinew]

Can someone please explain how to do these the answers are highlighted

I did this for number one but idk it just doesn’t seem right

Even though it got the answer

[summer ruin]

what do you think about inequality e^(3x) >= -1

[hushed sphinx]

2 must be a typo or something extremely weird going on.

[fiery sinew]

Oh yeah sorry it was arcsin I miss wrote the question now it makes sense

[fiery sinew]

Isn’t it always greater than -1 and never equal

[summer ruin]

I think you can say more, but sure

[fiery sinew]

So is this the better way to justify?

[summer ruin]

yes

[fiery sinew]

Ok thank you

[rain marten]

i just realised that e^x has no roots, and e^x = 1 + x + ½x² + ⅙x³ + ...
does this mean that this is a polynomial with no roots???

[hushed sphinx]

No, because a "polynomial" by definition has only finitely many terms.

[viscid thistle]

try going for substitution

like let e^-x/2=t

then find the value of dx

substitute it

and also

take log both the sides

will help u

[rain marten]

oh that's really anticlimactic

[strong verge]

can someone quickly tell me what transformation -f(-x) is ? bc how is it a reflection in both axis

if u multiply it out its just f(x) which is the og function but thats not the answer

[hushed sphinx]

You can only "multiply it out" like that if the function happens to be odd.

I don't think it has a name. It's something you can do with a function. Rotates its graph 180° around the origin.

[frosty laurel]

yupp ty

[fallen sequoia]

how did they get to costheta + isintheta? i understand the magnitude |z|

i must have forgot my trigonometry

i'm struggling to understand why the x coordinate is given by |z|cos theta lmfao

[hushed sphinx]

(cos(theta), sin(theta)) is the standard parameterization of the unit circle in the R^2 plane, this just expresses that as complex numbers instead.

[fallen sequoia]

huh i see, i think i understand

this has always been a concept that i've overthought

[hushed sphinx]

In other words cos(theta)+i sin(theta) is the complex number corresponding to where the point where the fat arrow in your diagram crosses the unit circle.

[fallen sequoia]

hmm ok, thx

[viscid thistle]

anyone familiar with this theorem

[normal coral]

#calculus

[viscid thistle]

this is definitely not calculus

this is about finding roots

[worthy bridge]

ok thug

how is my answer wrong tho, my teacher is fucking me over

bro what.. i asked for help not a life story

nice one

[uncut mulch]

"standard form" is ambiguous
in this context, they probably mean vertex form

[normal coral]

idk if I am just an idiot but last time I checked, $f'(x)$ is calculus

[obsidian monolith]

saddayyy_

[viscid thistle]

in the context of this, sturt theorem is part of algebra and polynomials. It's just euclidean algorithm involves a tiny bit of derivative.

but it would still be really off to just refer to calculus whenever you see a derivative signs i suppose

cause many other math topics use the concept of derivative

it is simply introduced in calculus formally

[normal coral]

yes but at least what I have seen in most us precalc courses, they only introduce the differential quotient and the concept of a limit which is why I was saying that looks more akin to higher than precalc

[viscid thistle]

I am in G11 and this is taught to us in our study of polynomial equations

[normal coral]

ah ok

[viscid thistle]

related theorem taught is one called descarte's rule of sign, which I think is very similar

also about finding real roots with different amounts of sign changes in a polynomial

[vast quartz]

so you learn calculus in precalculus

[normal coral]

@viscid thistle if u don't mind me asking, are u in the us, or international?

[viscid thistle]

I'm in Asia

[normal coral]

ah

so I would put that in #calculus as that does involve some differentials that are not taught in the normal us precalc curriculum

or in the help forum

when in doubt

[viscid thistle]

ok

[novel sparrow]

I hate web assign it’s been a nightmare this semester

[lunar viper]

because cos(theta) would be on a unit circle. for larger or smaller lengths, you must multiply by the magnitude aka hypoteneuse length in this case

[lone yoke]

Hi can you guys help me with this?
1.How is the equation of an ellipse determined when the foci and vertices are given? (Note that the term "vertices" refers to the endpoints of the major axis.)

2. Is it possible to determine the equation of an ellipse when the coordinates of the endpoints of the major and minor axes are given? If so, explain how.

[remote mesa]

I remember having more web assign hw than actual hw, I wasn't able to learn at all from it, actually it made my math worse cause I was just grinding out pointless problems pointlessly

Math software is literal hell

I didn't learn until I put the pencil down and tried to figure out easier ways to solve the same problems and why I struggled

[novel sparrow]

I am assigned like 50-70 different types of questions a week plus a quiz I only get 1 shot at within 5 hours.

I get 1 shot at exams within 2 hours.

I shouldn’t make excuses, but this isn’t learning math it’s like basically weeding students out and meeting deadlines

I have to agree with you 100%

[remote mesa]

It's completely stupid. You'll be so burnt out you won't have any energy left to learn or retain

[novel sparrow]

50-70 questions isn’t necessarily bad. Studying for exams over 100’s of questions that is

[remote mesa]

It's that + everything else on top of it

In my case our lecturers barely could speak english

I got further teaching myself and being lazy

[novel sparrow]

What class are you taking

[remote mesa]

Being lazy can be good for retention sometimes actually

Right now I'm being gatekept by academic standards so I'm taking more algebra in a different program

This time we don't have a teacher or a book lmao

But I have the cheat codes already

[novel sparrow]

Yeah that sucks, web assign sucks. I am taking calculus. Homework isn’t bad, quizzes aren’t bad.

The exams fuck lol

The exams are like the only thing that matters it’s like 70% weighted

[remote mesa]

Some schools expect most of their students to fail higher math courses

[novel sparrow]

I’m in college btw

[remote mesa]

I'm starting to see why the US has such low scores now

[novel sparrow]

I like this formula sheet for algebra it pretty much has a majority of what you will need.

My biggest gripe with webassign is that they ask so many word problems they should probably focus on more pure mathematics in my opinion

[remote mesa]

That's a damn good sheet

Well to be fair word problems are supposed to be the hardest ones to solve but some involve trickery or wordplay

[remote mesa]

If you have other stuff like this for any other topics, even if not math related feel free to send them my way

[novel sparrow]

EEweb has a ton of those cheat sheets you really don’t need anything else for math besides personal notes from homework and practice.

The only other topics I touch on now are spirituality tbh I don’t think you would be interested in that if you are academic enough lol

[remote mesa]

All knowledge is sacred

We are also using algorithms written by leaders of ancient cults

[novel sparrow]

Yeah there definitely is a lot that has originated from religion and cults that we use. I’ll share some math connections I made if you really want in dms. I don’t feel comfortable sharing in this server

[digital mirage]

why we took n -----> infinty ? fucntion is bounded b/w [a and b] does n-------> means infine partion ofr maximum accuracy ? or not then why n is approaching infinity ?

[summer ruin]

because you can't measure area under the curve with finite number of rectangles

as a consequence the width of each rectangle is reduced

[whole nimbus]

Does anyone have any worksheets they could send me about transformations of functions AP precalc?

[hot holly]

Can someone explain this form of the binomial theorem is (with the floor n/2 and n choose 2k). You can ignore the cosine and sine (problem was about finding a polynomial with roots of cos2kpi/n)

[warped cipher]

#calculus

I've never seen binomial theorem in precalc

[vernal pine]

Aakarsh and Claire were just in math class together, but they have different destinations.
Aakarsh sets out at 1:30 PM, immediately after class, headed due north at 11 feet per second. Claire stays
behind for 15 minutes to ask the instructor a question, and then sets out due east at b feet per second. What
is the lowest number b can be that will make Aakarsh and Claire coincide?

Im having trouble figuring out how to find it

[hushed sphinx]

If they're going in different directions, then it sounds like no b will ever make them coincide ...

(Unless Aarkarsh contrinues straight ahead after he reaches the north pole and then moves south until he meets Claire who has gone the other way around the world).

[jagged vine]

can somebody walk me through this?

please

[slim steppe]

You have your x value (8) and your y value (3). So 3=Log base a of 8

So what is some value that you cube it to get 8

2

So your a is 2

So it will be y=log base 2 of x

[jagged vine]

ty that makes sense

[viscid thistle]

Does precalc help you with calc?

[blazing hearth]

.

[viscid thistle]

Nope, the school system sets it up to delay fast learners and drag out the education process

Purposefully makes it a difficult checkpoint for even advanced learners to diminish their mathematics confidence

[slim steppe]

Well said

[viscid thistle]

oh no

luckily I will only be taking 9 weeks of it

becuase my second semester is trig/precalc

i’m on alg 2 now

it was more satire but ok

👍

gl!!

[carmine aurora]

Can someone explain how it goes from 1+cos=4-4cos*
To 4cos*+cos-3=0

[raw hill]

Subtract $(4-4\cos^2 \theta)$ from both sides

[obsidian monolith]

Civil Service Pigeon

[carmine aurora]

Thanks

[dapper estuary]

I don’t understand the second step

What does performing the inverse function mean?

[summer ruin]

logarithm and exponential function are inverse functions of each other

[sullen jewel]

please answer this general form to standard form

[slate crane]

divide by 8 on both sides to solve for y, then separate addends on other side to get standard form in terms of y=mx+b

[sullen jewel]

wow i dont get it sorry im not good at this

[slate crane]

wait to start off, you need it in this form yeah? y=mx +b

[sullen jewel]

ye

[slate crane]

okay so you pretty much already have it in that form: mx+b=y
but y has a coefficient in front of it, so you divide by 8 on both sides (cause what you do to one side, you always have to do it it to the other)

[sullen jewel]

y = x^2/8 - 2 ? is this it?

[slate crane]

yes sir

@sullen jewel ^

[sullen jewel]

so this is the standard form @slate crane ?

[slate crane]

yes, but some schools use Ax + By = constant

[slate crane]

oh I totally didn’t see that it was an x squared, your answer is 100% right. just the formula for standard form is y=ax^2 + bx + c whereas the formula I supplied previous is for a linear line. yours is a parabola where a=1/8 (coefficient of x^2), b=0 (coefficient of x, since you don’t have an x variable), c= -2

[vast quartz]

uh

me personally, i'd rather not start calc without knowing any trig or college alg concepts

ive been self studying a bit of precalc and it's only made me more confident

[viscid thistle]

I was joking, but even then personally my hs teaches trig concepts in alg 2

[normal coral]

is there any pretty notation denoting that f(x) is symmetric to the y-axis other than:
f(x) is symmetric to the y-axis

I doubt there is but just wondering

[normal coral]

im pretty sure all algebra 2 courses at least have some basic trig (from at least what I have seen)

I mean ofc there are gonna be some out there that don't but I'm pretty sure most do

[dapper estuary]

I don’t understand the second step

Please explain me how it got there and what performing an inverse function is

[summer ruin]

log and exponential are inverse functions of each other

[drowsy cypress]

@normal coral

Even Function - Symmetric about y-axis
f(-x) = f(x)

Odd Function - Symmetric about origin
f(-x) = -f(x)

[lunar viper]

really depends on who's asking

[normal coral]

yes, that is the definition. not a notation though.

[warped cipher]

remix?

[dapper estuary]

Ye? What’s up

[warped cipher]

nah just wondering what the heck is remix next to your name

thats a new thing?

[young sable]

Guys

How do you do rational function word problems

[solid pilot]

Post your question

Explicitly

[sage lichen]

Can anyone help me?

[dapper estuary]

Yes I think so. It’s there because I edited the picture before I posted

[warped cipher]

you can ask here or #❓how-to-get-help

[fast kiln]

how would you identify whether a function, for a given domain, is an increasing function or decereasing function, or neither? For this question, I found the first derivate but then I don't know how to determine the type of function

[summer ruin]

if the derivative is non-negative, then the function is non-decreasing

if it's non-positive then the function is non-increasing

[warped cipher]

<@&268886789983436800>

[hollow hedge]

Thanks

[rain palm]

my teacher didnt give the reasoning as to why a cubic is guaranteed

if anything that plotted out looks like a parabola to me

[hushed sphinx]

The strange thing is that the table gives the coordinates of five points, whereas the text claims there are only four ...

And according to Wolfram, the simplest polynomial that passes through those particular five point is of the fourth degree, which is not even among the options.
https://www.wolframalpha.com/input?i=interpolating+polynomial+{{-3%2C10}%2C{-2%2C7}%2C{0%2C2}%2C{2%2C8}%2C{4%2C12}}

[sage lichen]

help anyone

||@Helpers||

[small hatch]

How do I find U1 in a geometric sequence if all I have if U7=24 and U15=384?

[long hearth]

Bro what even is dy/dx

[icy star]

notation for the derivative of y with respect to x

[solar olive]

those two form linear system with two variables and two equations

[long hearth]

what if we derived x with respect to y would it create a black whole

[icy star]

no

[long hearth]

darnit

thought i was onto something

[normal coral]

if you are familiar with the notation of $\frac{\Delta y}{\Delta x}$, you can think of $\frac{dy}{dx}$ as an infinitesimally small change in y over an infinitesimally small change in x.

[obsidian monolith]

saddayyy_

[summer ruin]

you can, but don't

[normal coral]

but be mindful that it isn’t exactly the same thing, it’s just an analogy that helped me learn the concept of a derivative

[brazen canopy]

Hey can someone help me out with this question

[normal coral]

I feel like as long as u think of it as an analogy instead of a mathematical definition, it's fairly harmless until you learn the formal definition

[summer ruin]

even then the analogy doesn't even make sense since there's no such thing as infinitesimal change in classical analysis

[pine geyser]

First step is to find "b", you know that the first month is going to be:

ab^1=620

and the forth month:

ab^4=1083.

Now you should:
1.Divide these two equations in order to find b (ab^4/ab)
2. Now that you have b, put that in one of the equations, and you will find a
3.then for the answer obviously: ab^24 = ?

The numbers are really messed up

[raven stone]

did anyone help in the end?

[sage lichen]

nah

[sage lichen]

dawg i thought u was gonna help me. :/ 😦

[raven stone]

im not sure how useful id be LOL 😭

[pine geyser]

I can help you with that

[pine geyser]

I will explain the second one

We got two points from the exponential function which one of them is (0,18) and the other one is (4,2):

When g(0) = 18 so:

ab^0=18

And we know that every number that has the power of zero would equal to one. So you can find out the value of "a".

Now we will use the second equation (4,2)
Now that you know the value of "a", you can easily find the value of "b" using g(4).

[pine girder]

did anyone answer the first question

@sage lichen

because I can hel

p

[sage lichen]

maple did, i failed the second 1

[pine girder]

so you need help on the 2nd ?

@sage lichen

[sage lichen]

sure

[pine girder]

alr

we have ab^x

for x=0, ab^x=18

so ab^0=18

a*b^0 is the same as ax1

so a=18

all clear so far?

alr I suppose it is

18*b^4=2

b^4=1/9

b=1/root3

so we have ab^x=18(1/rt3)^x, which is the same as 18(1/3)^x/2

[sage lichen]

mhm

pr8 it

[pine girder]

?

[sage lichen]

appreciate it (pr8 it)

[pine girder]

ok'

np

[viscid marsh]

no dx/dy

?

[viscid thistle]

hii

im new here

i need serious help

[hushed sphinx]

The way to get any help is to ask some questions and not flail around in all the channels. See #❓how-to-get-help.

[raven stone]

that would be kinda cool

[brazen canopy]

Hey guys if anybody is in AP Precalc send me a dm we can help each other out yk

for future

[lament anchor]

Can anyone tell me what I did wrong?

[quick plinth]

is it x (3/2, 1/2)

or (1/2, 3/2)*

[quick plinth]

from 1/2 to 1 and 1 to 3/2, f(x) is negative

so for f(x) < 0, x is between 1/2 and 1, and 1 and 3/2. same as x is between 1/2 and 3/2

[long hearth]

Oh

[delicate bolt]

just started differntiation and i cant understand this chain rule man

i even tried yt vids and like i pretty much memorized it at this point but havent understood it

just having it memorized was working fine till i tried differntiating e^(x*ln(2)) and I couldnt

[uncut blade]

Have you seen 3 blue 1 brown's essence of calculus explanation?

[delicate bolt]

yep even saw that

helped a lot but

still not completelty there

[uncut blade]

Ah fair, that one helped a lot for me

[hushed sphinx]

Chain rule is soundly #calculus, not pre. But it would be easier to get useful help if you can state your confusion with more specific words than "I don't understand".

[delicate bolt]

Hm

[delicate bolt]

Ill try to rephrase it and thanks for correcting me

gonna give it a try myself again tho

YO WAIT I THINK I JUST GOT IT

[patent turtle]

number 4

help pls

[slim steppe]

What is it asking, do you think

[patent turtle]

oh dw i solved it

[slim steppe]

Yeah, I know. I saw in the calc channel

[patent turtle]

i was jus confused with the definitiion

[patent turtle]

yh

[lunar viper]

expected value of x as the function approaches x from the left

[last pine]

Guys, will there be eulers number on the test tomorrow

Also

If your trying to solve a exponential equation with (216^1/3)^5

[calm fractal]

anyone know why the 3 is a negative

nvm i know why

[torpid oyster]

cuz the drevative of cot is negative csc square

[digital mirage]

then how is this coming ?

is cos(x+a)=sin(x-a)?

[bitter compass]

can someone explain to me where 4sqrt(U) du was obtained?

[slim steppe]

Because 1+x/4 is set to u

[viscid thistle]

alright

given an exponential function how would you find its equation? (it can have any transformations but not horizontal transformations)

i mean like horizontal strech or shrink

[haughty tapir]

ello i wouldve just put the message in this channel but i didnt know it existed, heres my question

#help-35 message

[marsh cloud]

Fr

[fleet drift]

yo any way to visualise sin/cos/tan to make learning about it more intuitive?

[wraith tiger]

i feel so foolish how do i write the derivative of the inverse of function f

[balmy orchid]

why are people posting calc questions here

[viscid thistle]

you cant include 1 in your answer

[warm oyster]

i had to prove volume of sphere is equal to 4/3 pi r^3, i am getting 8/3 pi r^3

[red knot]

And

What do you want

A cookie?

[warm oyster]

huh?

oops

@red knot

[hushed sphinx]

I think you want (or at least need) some time to find your missing civility. Come again tomorrow.

[warm oyster]

,, \mathrm{V=\pi \int_0^{2R} {R^2 \cdot dR}}

[obsidian monolith]

Yajatjamal

[warm oyster]

this is what im solving, i did a cylindrical element

[analog flower]

having R in the integration variable and in the limits seems sketchy to me

[warm oyster]

yea me too

this is what i tried to do

[warm oyster]

<@&286206848099549185>

[warm oyster]

wait

it should be

,, \mathrm{V=\pi \int_0^{2R} {R^2 \cdot dr}}

[obsidian monolith]

Yajatjamal

[warm oyster]

maybe something else

,, \mathrm{V=\pi \int_0^{2R} {P^2 \cdot dr}}

[obsidian monolith]

Yajatjamal

[warm oyster]

this one is right

[warm oyster]

(nvm got it)

[vast quartz]

I'm somewhat doubtful this is precalc

[warm oyster]

y?

[vast quartz]

Idk there's just something about it

Could be the integral but idk it's at the tip of my tongue /s

[hot holly]

Lmao my AP calc class hasnt even taught this yet

[hot holly]

Can someone explain how they do this

[analog osprey]

can someone tell me why it isnt also associative

[late basin]

I've gotten this far but don't know how to rationalize it

[prisma oriole]

anybody know how to find the time that the ball is in the air?

[vapid plaza]

It is also associative

[rotund crystal]

Why do even functions bounce back even when they're below the x-intercept? Like doesn't any negative number when raised to an even power become positive

[elfin matrix]

$ln(2i\pi\times e^{2i\pi})=ln(2i\pi)+2i\pi$

[obsidian monolith]

caffeine

[elfin matrix]

is this correct?

$ln(2i\pi\times e^{2i\pi})=ln(2i\pi)+ln(e^{2i\pi})$

[obsidian monolith]

caffeine

[elfin matrix]

going off the idea that the ln and e cancel in the last term of the equation

[elfin matrix]

wolfram alpha says this is incorrect

[pine geyser]

which direction does the parabola go? what do you think, is it up or down?

[fiery cobalt]

8/3 pi R^3

[prisma oriole]

its reflected but already got help 🙏

[pine geyser]

alright

[gaunt glen]

:orz:

[timber spindle]

Has anyone here done calc 2?

[past grotto]

Hi...any study room?

[sleek laurel]

elaborate

[green mulch]

split the sum, as i=0 to floor(n/2) and i=floor(n/2) to n, you'll see some symmetry

[hot compass]

Calculate the mobility of electrons in copper at a temperature of 0°C, if the specific thermal conductivity of copper at this temperature is 414.8 Wm-1K-1 and the concentration of electrons in copper is 8.427.1028 m-3. Start from the Wiedemann-Franz law.

Constants: e=1.602.10-19 C I k=1.38.10-23 J/K
help plz