help-39

[silver sequoia]

Uhmm

[merry carbon]

In that, you just can work out
[
\qty( \lim_{x\to 0} \frac{\sin(3x)}{\sin(x)} ) \qty(\lim_{x\to 0} \frac1{\sqrt{1 + \sin(3x)} + \sqrt{1 - \sin(3x)} } )
]

[jolly parrot]

@merry carbon

[silver sequoia]

Ohh hmm

[sinful nebula]

as i told, divide by x in both numerator and denominator

[silver sequoia]

Where does the 6 on 6 . Sin3x/3x go?

[merry carbon]

I just rewrote the original limit you wanted, and cancelled the common factor of 2 from numerator and denominator, at which point you can do the whole "divide both numerator and denominator by x" thing

[silver sequoia]

Ohh

Hmm

So uh

If i have done it like this..

Now i can just use standard limits?

Uh

[sinful nebula]

yes

[silver sequoia]

Ohh hm

[sinful nebula]

all the methods mentioned before produces the same answer

try to solve using different methods

it will benefit you

[silver sequoia]

Why do i get ..

[sinful nebula]

you will get 3x +1

and 1-3x

[sinful nebula]

under root

[silver sequoia]

Ohh

[silver sequoia]

Like that?

[sinful nebula]

like this,

[silver sequoia]

So its 6 ÷ 2?

[silver sequoia]

What do i do with the 1 ÷ 2 on the left side?

Oh

[sinful nebula]

multiply

[silver sequoia]

Multiply it

[silver sequoia]

Right, so its 6÷4

= 3÷2

[sinful nebula]

3/2 simplified

[silver sequoia]

Thankyou yall

😭

[sinful nebula]

try

[silver sequoia]

Tysmm

[sinful nebula]

to solve using other methids

told earlier

[silver sequoia]

Oh?

[sinful nebula]

like it will benefit you

if one method fails (or hard) you can try other

[silver sequoia]

This?

[sinful nebula]

wai

[silver sequoia]

Dont worry

[sinful nebula]

yea

[silver sequoia]

Oh

[silver sequoia]

What do i do next?

[sinful nebula]

hmm

i will have to do in my book

[silver sequoia]

Ohh hm

[sinful nebula]

dont substitute under root ones yet

maybe try breaking fractions, simplifying. but its too much calculation

stick with standard limits. Sometimes substituting can make the problem confusing or lenghty

@silver sequoia any more questions

[pearl pond]

@silver sequoia Has your question been resolved?

[pearl pond]

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[hollow siren]

Hi! I'm relearning algebra and I'm confused as to why the following is not the correct answer by my teacher. Pardon my poor handwriting

[hollow siren]

According to my teacher the correct answer is:
\frac{2a^2b + 3ab^2}{b + 2a}

[plush bramble]

you just need to distribute the ab to (2a + 3b)

ab * 2a = 2a * ab = 2 (a * a) b = 2a^2 b

[hollow siren]

But why is the a and b term added to both sides? I feel like I'm missing some basic information here that I'm not getting

[plush bramble]

$\frac{x}{y} \cdot c = \frac{cx}{y}$

[hollow siren]

So I understand that the left term becomes 2a^2 because a*a but why is the b added? And same with the right side, it gets an extra a

[jolly parrot]

riemann

[plush bramble]

if x = 2a + 3b, and c = ab, what's cx = ?

[hollow siren]

cx would be ab *(2a + 3b)

[plush bramble]

ab * 2a = ?

[hollow siren]

ab * 2a = 2a^2b

I SEEEE

Thank you. What is this called?

inb4 "multiplication"

[plush bramble]

?

[hollow siren]

Like why do I need to do it to both terms here

[plush bramble]

what is "it"

and what is "do"

and what are "both"

[hollow siren]

Well I'm terribly sorry, I don't know the terms for this in English that well. I'm just confused why do I need to perform this multiplication operation to both sides of a plus calculation, but if it were a multiplication ab(2a * 3b) it would just simplify to 6a^3b

[plush bramble]

x * y = y * x for all numbers x, y

similarly, x * y * z = z * y * x = ...

[hollow siren]

So 3ab^2 = 3b^2a

[plush bramble]

and c * (x + y) = cx + cy for all numbers c, x, y

[hollow siren]

What is the name for this rule so I can look it up? x * y = y * x

[plush bramble]

https://www.macs.hw.ac.uk/~markl/teaching/IUM/Axioms.pdf

[warm sonnet]

That 2 is your exponent

[hollow siren]

yes

[hollow siren]

I see, so commutative I guess? Thanks!

[warm sonnet]

You can't just multiply a to the exponent

[hollow siren]

But 3ab^2 = 3b^2a, they are equivalent, right?

[warm sonnet]

Plug in numbers for a and b

You won't get a true math statement

[hollow siren]

3 * 5 * 6^2 = 3 * 6^2 * 5

Both result in 540

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[warm sonnet]

Mb 🤣

Read the equation wrong

[hollow siren]

No worries, thanks for help!

[pearl pond]

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[wispy ridge]

im kinda confused about derivatives

is a function's derivative like the rate of change (speed) of a function extracted from its overall profile

[wispy ridge]

so like if I have a curve

and I just want it's speed

I can just take the derivative

[lost flax]

Yes

[lost flax]

I don't understand the part of its overall profile

But the derivative is like the speed

That's the idea

[steel dagger]

momentarily speed yeah

[wispy ridge]

So the derivative function has the slope of every instantaneous point

so like

if the derivative function is linear than could you technically make seperate functions for each slope

Ik this is kinda dumb but I just wanna make sure

[wispy ridge]

like a quadratic is going to reach values faster than a linear function since it curves

does derivative just capture that speed

[lost flax]

The derivative of a quadratic is a linear function

Because it gets faster the further you go

And that is reflected in the fact that the linear function, which is the derivative, becomes larger and larger

Value of the derivative = speed of the original function

The larger the derivative, the faster the function grows

[wispy ridge]

what is the value of the second derivative in relation to the original function

[lost flax]

It's like the curvature

Or at least it's related

In physics it is the acceleration

Thise two are the usual intuitions for the second derivative

[wispy ridge]

wdym by curvature

like

[lost flax]

Consider the curve of the function

If it is a very narrow curve at some point, then the second derivative will be larger

And if it is very wide and almost looks like a line, then the second derivative will be close to zero

It is not a perfect analogy but it works in most cases

For example f(x) = cos(x)

f''(x) = -cos(x)

You can see that the curve of f(x) gets narrower when f''(x) = -cos(x) = ±1, and it is almost a line when it is zero

Like it changes its speed faster

[wispy ridge]

cosine being a derivative of sine doesn't make any sense to me

on the graph it's like when sine is going up cosine is going down

or something like that

well

almost

[lost flax]

No, sin is going up when cos is positive

[wispy ridge]

maybe I'm thinking about it wrong

[lost flax]

That's why cos = sin'

[wispy ridge]

ok tysm I feel that I understand the 1st derivative a little more clearly at least

[lost flax]

Glad I was helpful

[wispy ridge]

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[high geyser]

Hello i got everything correct but i dont understand what a orthogonal trajectory does

when i plot the graphs it looks like this but how doe sthe purple function represent the orthogonal trajectory of the green line

[pearl pond]

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[ivory shadow]

how to determine Opposite, adjacent in this ?

[dense jasper]

,w plot (-7, 24)

[jolly parrot]

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[dense jasper]

$\theta'$ denotes the reference angle of $\theta$ btw

[jolly parrot]

Civil Service Pigeon

[ivory shadow]

thank you!

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[vital wasp]

I used integral test for b and got this for the integral, does this diverge or converge?

[dense jasper]

you forgot dn on these

this should be written as a limit

and don't do arithmetic with infinity

but since you get a finite value at the end, the integral converges

[vital wasp]

Nvm thanks @dense jasper

[vital wasp]

Ok

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[twilit brook]

How do i intergrate arcsin(x)

[dense jasper]

https://artofproblemsolving.com/community/c7h597221p3543950

[spare lark]

Ibp

[twilit brook]

What is that

[spare lark]

Integration by parts

[spare lark]

Graph theory pfp ?

Cool

[dense jasper]

taken from one of my test questions

I thought it was nice

[spare lark]

Matrices useful for this

I mean in general graph theory

Not specially the exercice

Anyway, u see @twilit brook

?

[twilit brook]

Yes i checked it out

[pearl pond]

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[viscid mural]

When I know the angle and opposite of a right triangle I use sin function but if I know the angle and hypotenuse I would use tangent?

[viscid mural]

I don’t need help with a specific problem just with trig functions in general

And when to use which function when I have a right triangle with a known angle and one side

[leaden wadi]

That depends on what value you are trying to find.

SOH-CAH-TOA.

[viscid mural]

Ok I have a question with the opposite given

[plush bramble]

,tex .sohcahtoa

[jolly parrot]

riemann

[viscid mural]

Idk if I would have to find adjacent or hypotenuse because I need both

Ty I have that down in my notes

[leaden wadi]

If you have the opposite, then you need TOA to find the Adjacent side and SOH to find the Hypotenuse.

[viscid mural]

Ok thank you that’s all I needed!

Oh wait it doesn’t even matter what I find first

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[glossy gulch]

Why are there two solutions? I've used my scientific calc and it only gave me 36.9. How would i know if theres another solution?

[dapper kraken]

can you show what you put on your calculator?

[glossy gulch]

yepp

[midnight haven]

Intuitively, if you move the line EF at the pivot F clockwise until EF and FG are parallel, the area becomes 0. Similarly, when we rotate it counterclockwise, we eventually get 0 once they are parallel. So, it goes from 0 to a maximal area and to 0 again, so at 2 different points it has an area of 45.

and it corresponds to the two different angles

[glossy gulch]

so does that mean all triangles have 2 different angles?

[midnight haven]

there is one case, where the area is maximised, only one angle satisfies the assumptions.

[glossy gulch]

so i would use a class pad to solve this

[dapper kraken]

afaik sin^-1 has the domain for -90 to 90

[glossy gulch]

ohhh

thank you so much for your help

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[dapper kraken]

actually sorry, its range is -90 to 90

[dapper kraken]

.close whoops

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[rustic cargo]

Did I set it up wrong, Desmos makes it seem like it might have a value

My thought was using l hospital rule

But couldn’t find a way to set it up

Been stuck on this problem for a day

Unless I’m overthinking it and infinity is the correct answer

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[crystal charm]

Can someone explain to me what was done in this step?

[crystal charm]

I do not understand how they got 58800 or (y+4)(4-y)

[tall flint]

or (y+4)(4-y)
they got here by multiplying by 2/2, so (y/2+2) becomes (1/2)(y+4)

the 58800 comes from multiplying all the numbers together hopefully

,calc 10009.812/2

[jolly parrot]

Result:

58800

[tall flint]

nice

[crystal charm]

I do not understand what was multiplied by 2/2

[tall flint]

the entire integrand

[crystal charm]

why did they do that? I don't know how I would decide to do that in the future

[tall flint]

you don't really have to do it

you could get away with moving the constants outside and leaving the terms with y as-is

[crystal charm]

thank you.

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[faint kiln]

Jaime's total pay for a 6-hour work day can be computed by multiplying the amount he gets paid for assembling a grill by the number of grills he can assemble. Write a function to represent the total amount Jaime will be paid if it takes him h hours to assemble each grill.

[faint kiln]

Helppp

[summer imp]

Well he has 6 hours total to do his job. How many grills can he assemble in those 6 hours if it takes h hours to make one grill?

[faint kiln]

ermmmm, p(h)=6h?

[meager trellis]

so if we put in h = 2 as an example

[faint kiln]

p(2)=12?

[faint kiln]

<@&286206848099549185>

[merry carbon]

if it takes 2 hours to make each grill, how many can you make in 6 hours?

[faint kiln]

3

[merry carbon]

Yep, and say if it took you, instead, 1 hour to make each grill, how many grills can you make then in those 6 hours?

[faint kiln]

6

[merry carbon]

Yep how did you work those out?

[faint kiln]

p(h)=6h <--??? ermm

😭

[merry carbon]

Not quite, no that would mean that you would've gotten this one, as 12 instead

[faint kiln]

Could you tell me and explain how you got it, i mentally give up 😭

[merry carbon]

We aren't supposed to

Here's one more then, say it takes 6 hours to make one grill, how many grills can he make in those 6 hours?

[faint kiln]

wait is it p(h)=6/h??

[merry carbon]

Yep that's it!

[faint kiln]

So that's the equation for the entire thing?

Cause my teacher posts the answers online to let us check and what she put was completely different to that

she put (a x p)(h)=90/h+72

[merry carbon]

Not quite, that tells you how many grills he's made, but you need to also multiply by how much he gets paid for each grill

Do you have a picture of the full question or something?

[faint kiln]

This is it

I don't know where the hell she got 90 and 72 from

[meager trellis]

ok yeah that sounds like either there's more context somewhere else (like is this meant to be a continuation of question 15??) or she just... made numbers up for some reason...

[faint kiln]

Ohhhh

mb

here it is

[meager trellis]

oh ok that makes a lot more sense

right so yeah, 6/h is the answer to question 14

and then 90/h + 72 is taking into account how much he gets paid for each grill

[faint kiln]

OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

I feeel sososo dumb rn

I am sorry you all thank you for your help

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[blissful cloak]

are there any odd numbers greater than 6?

[pearl pond]

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[clear orchid]

Need help with a show that questions

[clear orchid]

this is the original question

here’s what i’ve attempted

i’ve taken the derivative so far and have the relation between that greek symbol and i not sure where to go from there

[proud kiln]

Sorry to distract, but I love your handwritingn

[clear orchid]

thank you

[plush bramble]

Delta is just a constant. Treat it like 5

,w diff x * (e^(c/x)-1)

[jolly parrot]

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[pearl pond]

@clear orchid Has your question been resolved?

[clear orchid]

pretty sure my derivative is correct

not sure how to show that i^(m+1) < i^(m)

[plush bramble]

What's i=?

[pearl pond]

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[clear orchid]

is interest rate

this question is from a financial maths course

to do with specifically with annuities

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[sharp smelt]

here, I just have to prove that $\bigcup_{i\in \N} [i,i+1]$is $[1,\infty)$ irght

[sharp smelt]

essentially

[jolly parrot]

Veni, vidi, perii

[sharp smelt]

or do I first prove $\bigcup_{i\in I} A \times B = \bigcup_{i\in I} A \times \bigcup_{i\in I} B$

[jolly parrot]

Veni, vidi, perii

[sharp smelt]

oops

that's flase

is it not

hmm, this is hard

Every real number is basically crossed with every other number in [1,infty)

right

[fallen cipher]

Note that only the [i,i+1] is indexed.

Try drawing a picture first

R×[1,2] is a strip

[sharp smelt]

I don't quite follow

[fallen cipher]

Write out a few terms

R x [1,2], R x [2,3], R x [3,4] and then union them. Repeating this for a few times and see what the answer might be

[pearl pond]

@sharp smelt Has your question been resolved?

[sharp smelt]

$R \times [1,\infty)$

[jolly parrot]

Veni, vidi, perii

[sharp smelt]

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[lusty pier]

hi guys. can you help me with a problem

[west sapphire]

!da2a

[pearl pond]

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

[lusty pier]

wait i was sending it lol

one sec

how did they rearrange it to get hv'? thats kind of confusinf to me lol

[pearl pond]

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[lusty pier]

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[bleak star]

If we have 3 machines and the first and second can done the job in 7.2 days, the first and third in 9 days and the second and third in 12 days how much days does it take for each of them?

[pearl pond]

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[mighty basalt]

I got the first 3, which includes vector direction for sum, but can't figure out difference

[pearl pond]

@mighty basalt Has your question been resolved?

[mighty basalt]

<@&286206848099549185>

Im not finding a way to get the vector difference of A - B

<@&268886789983436800>

[unborn abyss]

A - B is equal to A + (-B)

if you can convert them into coordinates that would be helpful

[mighty basalt]

Convert them into coordinates?

[mighty basalt]

That's what I did to get C. When I try to do the same for part D though tan-1(y/x) It says the answer is wrong.

[unborn abyss]

okay well A - B is the arrow from the tip of B to the tip of A

that is definitely not 70°

[mighty basalt]

Im still not sure how to really visualize whats going on.

I have that but not sure where the angle is coming from. tan-1 gives me 70 for (-13-8/-7.5). Which is how I got part B just positives for 13 & 7.5

I forgot this 😂

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[viscid mural]

This is trig introduction to trig functions

I’m trying to find the angle of problem 49

I know that I’d have to use cos from SOHCAHTOA

But when I do the inverse 134/182

My answer doesn't match the answer in the book

The angle in the book is given 50.7 but I got 42.5

I’m given the adjacent and opposite

Oh

Wrong

Trig

But I still get the wrong answer

Now I’m getting 37.1

Wait no

Sorry I meant I’m given the hypo and adjacent

I was looking at the wrong problem for 49 it’s opposite and adjacent

Which would be the tangent function TOA

I got the answer now I was looking at the wrong problems this whole time thank you!

Angle 50.7

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[elfin radish]

Some help I don’t know what I’m doing I think it’s 2y+3.75 but I don’t think I’m doing anything right idk even where to start

[signal atlas]

For 1 you did perimeter, not area

For 2 how did u get 7r+10

[elfin radish]

😭I wish I knew also could u explain how I would do area

I’m kinda struggling 😔

[naive pond]

For area, you simply multiply the length of the base of the rectangle times the height

You can get the equation $2.5(2y+1.5)$ from this

[jolly parrot]

747244351179980930

[elfin radish]

that explains so much than you i think i get it now

[naive pond]

Yw

[naive pond]

This is not the final answer but based on your other work I think you can take it from here

[elfin radish]

yes

Hello best friends ummm I wish I knew where to start but I messed up all of these and I have know idea what I messed up

[pearl pond]

@elfin radish Has your question been resolved?

[pearl pond]

@elfin radish Has your question been resolved?

[pearl pond]

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[tranquil badger]

1. Even though dividing the entire equation would divide the input so you could say itd still be equivalent that doesnt make sense because not only is the input changed but had you solved out the problem wouldnt many things not be commutative/distributive? And even then where exactly would they have undone this operation later?

2. I dont understand how subtracting things from both sides is somehow equivalent because no matter how i look at it all im seeing is they pretty much subtracted it twice being from the problem and then the result and even the subtraction in itself seems to be unequal or related to the problem shown.

[signal atlas]

Wdym by "dividing the entire equation would divide the input"

[tranquil badger]

https://media.discordapp.net/attachments/908078029778083872/1281050384420573214/image.png?ex=66da4ea4&is=66d8fd24&hm=fb8cfc723a9a9f7b5b83348931eadba6db161776905dc4a3fe8e5b1d06222a72&=&format=webp&quality=lossless

[signal atlas]

Yeah but how are you dividing the input? x is still there (which I assume is the input)

[tranquil badger]

Isnt each input being divided by X including those that are not inputs?

[signal atlas]

The input is not really being divided by x. This isnt a function so there isn't an input anyway. It is an equation.

The point of this is we are trying to find which values of x satisfy the equation. There are values of x that satisfy the equation, and there are values of x that will not satisfy the equation.

If some value of x does satisfy the equation, we know the left side is 0 for that value of x, and 0/a is still 0, so it still equals the right side. The equation holds. This will result in us being able to find the explicitly the value of x.

[tranquil badger]

pretty sure it is a function since its a quadratic and the point was to derive the quadratic formula

[signal atlas]

A function is a "machine" that takes inputs, and outputs something. "ax^2+bx+c=0" is just a statement. Something that is either true or false.

You can say something like f(x)=ax^2+bx+c is a function, but in this case we are looking at an equation

[tranquil badger]

alright

also i am about to drop math

because like

honestly the pain is just too much at this point and well

it isnt even the pain my motivation is infinite.

But its just how.

No matter how I try no matter how many days, weeks, or months pass by.

I cannot complete one topic.

I cant even make this subject flinch.

Its like when those anime characters give there everything but the enemy has a higher PL so they cant even damage them.

pretty much over at this point.

and even in this conversation its like

nothing changes.

so

[signal atlas]

Is this for school or are you working on this for your own sake

[tranquil badger]

thats probably all...

[tranquil badger]

work purposes as i wanted to go into IT

but i guess it was just not meant to be

because honestly

this is my personal hell

no ammount of determination can even make it move an inch.

and even if i do complete one it takes weeks or a month (impossible pace id be old by the time id finish)

i think i have dyscalculia because

in my younger years i simply was not disciplined and i dont blame myself for that considering circumstances.

oh well

thats all it is...

[signal atlas]

What are you using to learn? I don't want to deny your feelings, but I believe there a very few people who can't learn math if they put their mind to it, and you do not seem like somebody who is incapable.

Sometimes you need more than determination. Learning by yourself can be hard since you do not have the structure and incentives a school (sometimes) give. There are many other factors that may be holding you back from being able to learn.

If you can give some examples of topics you struggle with learning and why, I and other people here may be able to give more helpful advice.

[tranquil badger]

oh trust me... i think ive had enough of people here... and i honestly just think that

i dont say this often but when i was younger i simply didnt learn well... anything really

i mean

in other subjects some?

but math??? people had to cheat and buy my way through that

and by the time i finally.... became complete mentally

it just seems like its too late the damage is just so severe that

i believe i finally understand

you people you have a foundation to build all new concepts on and people who helped you and you also developed stronger associative reasoning due to your time and experience

i dont have that

for me i am well unfortunate

well, thank you for talking, I think that will probably be all.

its just... it... theres nothing i can do its been months now so.

well.. "I hoped their'd be stars.." see you around.

.close

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[wintry stream]

I hate math problems that seem like the answer requires digits but it has to be whole numbers, can someone help?

[austere ermine]

does anyone know what 1 + 1 is

[wintry stream]

2

[austere ermine]

11

[wintry stream]

Close enough

[austere ermine]

.

what even is this server tho

just maths?

[wintry stream]

Yes its maths

[austere ermine]

,

ima join gohars server

[wintry stream]

You're a helper right?

[austere ermine]

no

idek all this maths stuff

[wintry stream]

:/

[austere ermine]

its confusing

[wintry stream]

How are you helpers role

[austere ermine]

what

[wintry stream]

I think you're just messing with me

[austere ermine]

what

math is acually fun when you understand it

[wintry stream]

How do I physically do this question

Without using digits

[austere ermine]

3.1415926545323832

[wintry stream]

I cant use pi

[prime bramble]

the answer should not have decimal places

can you show your work?

it seems like you've made a mistake

[wintry stream]

I places -1 and 1 to remind myself that x1 has to be lower than x2

[prime bramble]

yeah, but what are your actual numbers?

[wintry stream]

I dont know what my actual numbers are, thats the thing

I subtracted 9 from the equation

Bc it doesnt help me find x1 and x2

[prime bramble]

why 9?

[wintry stream]

Wait a fucking minute

THIS WASNT THE EQUATION I WAS DOING

[clever turret]

[prime bramble]

[wintry stream]

the actual equation was 3x^2 + 12x + 9 = 0

[prime bramble]

right, okay

do a GCF first

it'll make your life easier

[wintry stream]

Im left with 3x^2 + 12x = -9

[prime bramble]

yeah, that won't help

keep everything on one side

[wintry stream]

Wait a minute

I completely forgot this equation looks like a uhh

What is that

X^2 + x + #

[prime bramble]

quadratic

[wintry stream]

I dont remember

Yes

Quadratic formula

If thats

What its called

[prime bramble]

well, that is one method yes

you can also just factor it

either method will work

[wintry stream]

Okay yea thank you for making me realize that

So x1 and x2 is just the opposite of a and b when I simplify it?

Nvm

H k

I think im gonna close this now

@prime bramble thanks for helping my frontal lobe think again

[prime bramble]

no problem haha

[wintry stream]

.close

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[hard locust]

Having trouble figuring out how to write this as an equation

[hard locust]

heres the original question

[pearl pond]

@hard locust Has your question been resolved?

[grim fractal]

looks like you have two regions

you need to find where y=sinx and y=cosx intersect

and then sum two integrals

[hard locust]

oh

[hard locust]

So this typa thing?

[grim fractal]

kinda but for one integral it's sin-cos, and the other is cos-sin

[hard locust]

More like this?

[grim fractal]

right

[hard locust]

Like this right?

[grim fractal]

No

sin and cos don't intersect at 0

[hard locust]

this is actually an issue i have with between the area problems in general, I am really bad at finding where points intersect in trig functions. I know its somewhere near 2/pi

[grim fractal]

set sin(x)=cos(x)

what value of x makes this true?

[hard locust]

i dont know this one

[grim fractal]

you can just look at a unit circle

or solve it algebraically

sin(x) = sqrt(1-sin(x)^2)

[hard locust]

pi/4

so the up bound is pi/4 for the the first part of the equation and the lower bound for the second part

[pearl pond]

@hard locust Has your question been resolved?

[hard locust]

What ya think?

[pearl pond]

@hard locust Has your question been resolved?

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[scarlet pike]

$(x^3 + 3x^2)/(x^2 - 2x - 15) = (4x+5)/(x-5)$

[jolly parrot]

prohipited

[scarlet pike]

This is my equation here

I'm dealing with rational equations in one variable

[cloud plume]

u can try to factorise thing ups and hope for nice cancellation

like x^2-2x-15

[scarlet pike]

give me one second i'm sorry

I am simply curious how we know that x CANNOT equal 5 and -3 here on my second step down

my work is sending right now

[random ermine]

cuz then the denom would be 0

[scarlet pike]

I don't quite understand what you mean

[random ermine]

you can't divide by 0

[cloud plume]

math do not allow u to divide by 0

[random ermine]

if x = 5 on the rhs you get 25/0

[cloud plume]

so u need to limit the range of x so that it does not contain 0 when simplifying from original expression

[scarlet pike]

the denominator would be zero?

OH

okay and the negative three is because of the left hand side, bottm portion, second parenthesis?

The one that I was able to cancel out

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[upper drum]

translate

[stoic imp]

find image of f

do you know what the image is?

@upper drum

[rough forge]

The domain is x <= 12

[stoic imp]

I'm eating croissant

how do you know that

I want to get into the nity gritty

[rough forge]

Ah bruh

lmao i fucked up so bad

[stoic imp]

which part specifically

[rough forge]

😂

So as x -> -inf there is no lower bound

[stoic imp]

do it in latex

[rough forge]

I cant

[stoic imp]

it's simpler

[rough forge]

Ok so I was mistaken

sqrt(12-x) is not increasing but decreasing so that makes matters not so obv as thought

[stoic imp]

which part specifically

[upper drum]

https://cdn.discordapp.com/attachments/1156825034963292203/1281237219125760030/wolf.png?ex=66dafca5&is=66d9ab25&hm=5ba37c50f73bda3025b6ead9b1ea474d5cfac6a6159636ff9847fef3a2c6e6a4&

[jolly parrot]

bacc

[upper drum]

neither dec nor inc

[rough forge]

Regarding the monotony of sqrt(12-x)

[jolly parrot]

bacc

[rough forge]

Which is trivial ||it's -infinity||

So there is no lower bound

Now we could try to search for an upper bound by finding a maximum

With the first derivative

[jolly parrot]

bacc

[rough forge]

You would do f'(x) = 0

To find that maximum

So the range would be (-inf, maximum of f]

[stoic imp]

I got lost

can you held me longer my hand

[rough forge]

yea

[stoic imp]

about the monotinicity of f(x)

how do I figure it out in general

[jolly parrot]

bacc

bacc

[rough forge]

The denominator is always positive and for x = 12 it is 0

So it really comes down to the numerator to figure out when it's increasing or decreasing

[jolly parrot]

bacc

[rough forge]

So at x = 8 there is the maximum

So f(8)

[jolly parrot]

bacc

[pearl pond]

@stoic imp Has your question been resolved?

[rough forge]

you can ping me if you have a question

[pearl pond]

@stoic imp Has your question been resolved?

[pearl pond]

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[timid quartz]

how do i do 2)b)?

[timid quartz]

im confused on how to get started

[cedar bough]

divide by the highest power of x

[timid quartz]

so in this case would it be x?

because root of x^2 would mean its x

[cedar bough]

no first simplify inside the root

factor out a x²

[timid quartz]

so it would be x^2 root (1-3/x)?

[cedar bough]

yes

now sqrt(x²) = |x|

since x i approaching -infinity, |x| = -x

sustitute it back

and solve ig

[timid quartz]

oh okay thank you

.close

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[candid rose]

Reopen

[next dove]

.close

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[cedar scarab]

It is given that there are 10 different English books, 6 different French books, and 4 different German books.

[cedar scarab]

I originally did it this way then realized it says "exactly one" missing. The way I did it, there is potential for there to be two missing languages. How can I factor in that one of the books has to be from the other pool?

[uneven perch]

alguém tem link de um bom material para estudar cinemática?

[pearl pond]

@cedar scarab Has your question been resolved?

[pearl pond]

@cedar scarab Has your question been resolved?

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[hollow parcel]

guys why the difference?

[cedar bough]

can you post the original pic

or question?

[hollow parcel]

well its just like in calculator

the task has to do with finance but

the bottom way is correct way to calculate

[versed ledge]

How are you getting first at 27.3??

[hollow parcel]

by putting it in calculator

[midnight haven]

in the above you just forgot a zero

[hollow parcel]

😮

[midnight haven]

27.3 is the result of 21*(1+0.3)

[hollow parcel]

😮

[versed ledge]

What calculator are you using

[hollow parcel]

the good one

which i cant use on test

first time i come on math exam

profesor tell me

no no you cant use this 1

it can do integrals

.close

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[vapid ivy]

Is this just undefined

Because sinx is 0

[midnight haven]

do you know the definition of a derivative?

[vapid ivy]

Can you help

[midnight haven]

do you know l'Hospitals rule

you see, sin 0 = 0, and 1- cos 0 = 0, so you habve a 0/0 in the limit situation, and in this situation you can use l'Hospitals rule

So you can just replace numerator and denominator by the derivative, then again evaluate the limit.

[vapid ivy]

Ohhh I’ll probs just watch a yt video

[chrome plank]

L'Hopitals Rule
$$f(a) = g(a) = 0 \implies \lim_{x \rightarrow a} \frac{f(x)}{g(x)} = \lim_{x \rightarrow a} \frac{f'(x)}{g'(x)} $$

[jolly parrot]

Shuba

[chrome plank]

Intuitively, you're saying, both numerator and denominator are zero, so which approaches zero faster?

[rough forge]

,, \sin(x) = \sqrt{1-\cos(x)} \cdot \sqrt{1+\cos(x)}

[jolly parrot]

bacc

[rough forge]

,, \lim_{x \to 0} \frac{1-\cos(x)}{\sqrt{1-\cos(x)} \cdot \sqrt{1+\cos(x)}}

[jolly parrot]

bacc

[vapid ivy]

Ohhhh

I get it now

[rough forge]

I was just saying you can completely avoid L'Hopital

[pearl pond]

@vapid ivy Has your question been resolved?

[pearl pond]

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[vagrant marsh]

So im doing this question here. And I was able to find that a is +- 1 and that c is sqrt(5), but im confused why its (+-1, 0) and not (0, +-1)?

[vagrant marsh]

nvm I just realised theres two forms of hyperbola

.close

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[copper pagoda]

(p,0)
(3pi,0)

so its continuous on the interval

ok ngl idk what im doing

0-0/3pi-pi

so the slope of the secant line is 0

but what does it mean if its not differentiable on the point (a,b)

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[rancid dew]

May someone help with with a math question about a Function graph and finding Lim x-> values and Vertical/Horizontal Asym, its a image

[wanton burrow]

For the first one

I think you just read the graph wrong

It’s saying

As x approaches infinity, the y values approach what

[rancid dew]

thats what im confused by

ive tried 3 and 0 for the first one

[wanton burrow]

what y value does the function even out at

at the far right side of the graph

[rancid dew]

wait so the lim x-> x f(x) is right sied to 0?

[wanton burrow]

no

I’m not using formal terms

uh

Idk how else to explain

but

At the highest x value

What does the y value approach

[rancid dew]

i figured it out thanks

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[gusty sandal]

I'm not sure how to simplify this function

[jolly parrot]

bacc

[rough forge]

Then you can use the difference of squares formula

[gusty sandal]

So it would simplify to (11/9)(1-sinx)?

[rough forge]

yes

[gusty sandal]

Then the limit would be 0 right?

plugging pi/2 in

[rough forge]

no wait

[rough forge]

it should be 1+sin(x)

[gusty sandal]

ohh ok because 1-sin^2x is (1-sinx)(1+sinx)

[rough forge]

1-sin(x) cancels with the

1-sin(x) in the denom

[gusty sandal]

yeah i kept just writing 1-sin^2x = (1-sinx)(1-sinx)

thank you

should (11/9)(1+sin^2(x)) go into the first blank then

yes its right thank you for your help @rough forge

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[silver sequoia]

Please give me hints

I don't know where to start. I only understand how to change if cos (pi/2 + x) but now i have no idea.

[silver sequoia]

(and the example (cuz im not native english, i might mistranslate your words, so i need example ))

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[glass schooner]

For some reason I calculated and evacuated the sum of this and I got 26 but the answer key said that it was 25

[kind heron]

sorry if im confusing this is in french but isnt this PEMDAS?

[glass schooner]

not to my knowledge no

[kind heron]

ok im gonna check it out

you are correct the answer is 26

would you like the explanation?

[glass schooner]

yes

[kind heron]

Start by calculating the product or quotient

Making it 33-1-7）2 ÷ 6+1）

Then determine the sign for exponential or radical expressions

Which makes i t33-7 2 (division sign)（6+1）

(The two should be small but I can’t type it)

Then calculate the power

= 33-49 (division sign) (6+1)

After calculate the sum or difference

making it 33-49 ÷ (6+1)

then calculate the product or quotient

= 33- 49 ÷ 7

Almost done, calculate the product or quotient

= 33-7

which is 26

sorry if i confused you english isnt my first language

[glass schooner]

oh ok

[kind heron]

did it help?

[glass schooner]

yeah

[glass schooner]

wait a second if english wasn't your first language then where are you from

[kind heron]

Romania

[glass schooner]

oh ok

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[sharp smelt]

Give an example of a function, where f(x^2) exists at 0, but not f(x)

[sharp smelt]

I was thinking of a function defined by y=-1 if x<-

y=1 if x>0

[acoustic path]

is your question asking about existence of a point, or existence of a limit at that point?

[sharp smelt]

limit

I'll quote it verbatium

just a minute

[acoustic path]

then your example is fine

[sharp smelt]

Giv an example where $\lim_{x\to 0}f(x^2)$ exists but $\lim_{x\to 0} f(x)$ doesn't.

[jolly parrot]

Veni, vidi, perii

[sharp smelt]

I have to prove the llimits are different now, do I not?

[merry carbon]

(you don't even really need an equals there: as the function needn't be defined at zero, and limits explicitly exclude the point you're taking the limit to...

[acoustic path]

that's my fault i was accustomed to the idea of a point before realizing

[merry carbon]

...incidentally, this is why I've emphasised the fact that the point you're taking the limit to needn't be included in the limit definition!)

[rough forge]

Maybe f(x) = |x|/x?

[merry carbon]

Well, "yes", but that's (actually) trivial

[sharp smelt]

That's effectively , my function>:kek:

[merry carbon]

(same thing )

[rough forge]

mb

[acoustic path]

it's fine it's just a more concise way of expressing it

[prime bramble]

there's one obvious choice for f(x) here haha

it seems like others have already all had the same idea though

[sharp smelt]

This took me a few days 😭

I mean a few days of revisting it

I was trying to come up with some sort of indictor function

[rough forge]

lol i saw it somewhere

[sharp smelt]

so here's what I was thinking of doing to prove the limit doesn't exis

$-\varepsilon<1-L<\varepsilon$
\
$-\varepsilon<-1-L<\varepsilon$

[jolly parrot]

Veni, vidi, perii

[sharp smelt]

adding them

wait

so $-\varepsilon<1-L<\varepsilon$
\
$-\varepsilon <1+l<\varepsilon$

[jolly parrot]

Veni, vidi, perii

[sharp smelt]

so $-\varepsilon < 1<\varepsilon$

[jolly parrot]

Veni, vidi, perii

[sharp smelt]

Am I overhtinking?

I think it might be easier to prove the LHL is -1

and the RHL is 1

yeah

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[sharp smelt]

thanks

[merry carbon]

(hence "trivial" )

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[idle lantern]

I'm taking an odes course and working through the chapter on separable equations, these are two lines motivating why were are allowed to us the method, I do not understand the step from the first line to the second

[idle lantern]

I understand that it uses the change of variable formula:

(from wikipedia)

The theorem looks almost similar but not quite

[versed mica]

y = g(x)

[idle lantern]

I think what's tripping me up is the fact the function f is a function of g(y), and the we have g which is a function of y and not x

[versed mica]

g’(x) = dy/dx

[west sapphire]

your y is a function of x

you might call it something like y = h(x) if you want to make it look more similar

unfortunate that g is being used for two different meanings in the two screenshots but hey

[idle lantern]

Okay, so in the first set of equations instead of having g(y) I'd have g(h(x)) and then instead of having dy/dx I'd have dh/dx?

[west sapphire]

yep, aka h'(x)

[idle lantern]

Perfect! I got it, thanks!

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[idle lantern]

.reopen

[pearl pond]

✅

[idle lantern]

.close

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[polar folio]

What is area of line AD when there's triangle ABC while AB=AC and point D is over line AB while BD =5 ,FC=13

[chrome plank]

can you draw that

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[polar folio]

It was this

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[sly plover]

What do I even do here

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[stoic imp]

I found S n T and basis S and basis H

how do I figure out the dimension of W?

oh, we can use the dimension theorem corollary

dim W + dim S n T = dim H

no? in direct sum the intersection is zero

my basis of H is dim 3

and dim (SnT) = 1

which if I didnt messed up should mean Dim W = 2

how do we find W ?

one of the three vectors in H is one of the two vectors in W

because W is a subset of H

no?

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<@&286206848099549185>

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[oblique sparrow]

how to simplify this?

[cloud zephyr]

hello TLancherGD!

[limber glacier]

$\frac{3^{2n+1}}{9^{n+1}}$

[oblique sparrow]

oh hi!

[cloud zephyr]

what have you tried?

[jolly parrot]

SilverSoldier

[limber glacier]

is it?

[oblique sparrow]

yeah

[limber glacier]

what have u tried

biscuity u can continue if u want to

[cloud zephyr]

its alrighty, you can take the lead 🙂

[oblique sparrow]

im removed n+1 and i got 1

but my calculator says this is 1/3

[limber glacier]

i just wanted to make sure i understood the expression correct lol

[limber glacier]

what do u mean u removed n+1?

[oblique sparrow]

,, \frac {3^{2}}{9}

[jolly parrot]

TLauncherGD

[oblique sparrow]

bruh

so, how to simplify this fraction?

[cloud zephyr]

I'm eating btw, but first hint would be
3^(2n+1)
we have brackets for the index, so... we need special operations to do it

[limber glacier]

whoops sorry i was occupied elsewhere

[limber glacier]

u cannot just remove the exponents like that

[oblique sparrow]

so thanks

its 1/3

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[vivid flax]

what does he multiply by to do this?

[midnight haven]

he just divided by -2

i think

[rough forge]

he divided the numerator and denominator by -2 on the left

[solar junco]

just divide the left hand fraction by -2/-2

left hand sorry

[vivid flax]

oh i see thanks

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[midnight haven]

what do i do if t=0

[midnight haven]

t is never 0, that's the idea of limits