help-13

[elder elm]

Can someone help me understand how they got their answer?

[storm mural]

do you know how to find that limit

lhopital or just seeing that e^n is dominant so it's ~ 3e^n/5e^n

[elder elm]

Yes, so this is my work:

[storm mural]

yes that's right

[elder elm]

Is this the nth term test?

[storm mural]

ya

[limber snow]

yes

[elder elm]

is my process right as well?

[limber snow]

nth term test == the divergence test

[elder elm]

I never use lhopital

[storm mural]

well you might justify that n^2/e^n goes to 0

[elder elm]

I just divide by common degree..

[storm mural]

but

[elder elm]

But how do I know when it goes to 0 and when goes to infinity for terms like these? Is it just whenever I see a constant divided by some strange value?

[storm mural]

normally you find goes to 0 by plugging the limit value in

direct evaluation

here you get inf/inf

we know e^n grows much faster than n^2 but this iskinda the use case of lhopital

[elder elm]

Still sort of struggling..how do we know it goes to 0? Am I just plugging infinity in for n and realizing this can grow exponentially?

[storm mural]

if you do lhopital you get 2n/e^n, then 2/e^n, = 2/infinity = 0

also, like, 100^2/e^100 is 0.000000000000000000000000000000000000000000000000000000000003

not a proof though

[elder elm]

🤔 ...Okay, for a problem like this though (asking me to evaluate the limit), it converges to to infinity...right?

[storm mural]

converges to infinity is called diverges

[elder elm]

I don't understand. How do we distinguish when something diverges or converges?

[storm mural]

diverges means limit doesn't exist or limit is +- infinity

[elder elm]

okay..

[storm mural]

huh wolfram disagrees with me

maybe limit to infinity isn't considered to exist

[elder elm]

I'm just confused on when to use the term "converge" or "diverge"...is it all subjective? For instance, for the problem above, wouldn't we say it converges to infinity and diverges from 0?

[storm mural]

oh, diverges from isn't a thing

diverges is just the opposite of converges

I would say it diverges

but maybe there's an argument for "it converges to infinity"

idk

[cedar kiln]

@elder elm Has your question been resolved?

[elder elm]

Hey still there?

[storm mural]

yes

[elder elm]

So is "converges" when it approaches a certain value?

[storm mural]

ye

a real value

assuming everything is real in your course

[storm mural]

I just said this to exclude infinity

[elder elm]

So isn't this arbitrary then? Like is inf not considered a "real value" here?

[storm mural]

it is somewhat arbitrary but converging to infinity is a little different from converging to 6, wouldn't you agree

by the definition of limits, goes to infinity is the same as doesn't exist since there's no number where the difference between all terms and it can be arbitrarily small

[elder elm]

Okay, so whenever it appears to be going towards inf, its diverging to infinity..

whenever it appears to be converging to any other value, it "converges"

[storm mural]

it's diverging, yes

[elder elm]

Okay, so let me eplain my thought process on some problems and lmk if I'm understanding it correctly.

[elder elm]

So the circled ones are the answers here

[storm mural]

mhm

[elder elm]

So these are for letter i...

[storm mural]

5/1^2, 5/2^2, 5/3^2, 5/4^2

[elder elm]

right..and I noticed they are slowly decreasing in value..

[storm mural]

ye

[elder elm]

does this relate to why its converging?

[storm mural]

terms converge to 0

[storm mural]

the terms have to have a limit of 0 if the series converges

but limit of 0 doesn't guarantee a convergence ofc

[elder elm]

Um

[storm mural]

whereas their sum converges to 5pi^2/6

[elder elm]

How about this..why is i converging and vi not?

[storm mural]

well, there's not exactly an intuitive explanation for why vi doesn't converge,

but the terms decrease slower

and it turns out you can slowly get infinity out of that

[elder elm]

So how would I be able to find out which converges and which does not?

[storm mural]

there are tests

in this case you would use, well, I learned it as the p-series test, idk if that's what everyone calls it

where sum of n^-p converges if and only if p > 1

could just as well be called the do we have to use the analytic continuation when we compute zeta at this value or are we fine using the direct evaluation test

there's several on https://en.wikipedia.org/wiki/Convergent_series#Convergence_tests

[cedar kiln]

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[vapid sand]

what should I be doing for 2b) i)?

wait nvm

.close

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[unborn cobalt]

I plugged in the limit straight into the underlined equation and still got 1 without using lhopitals. Is that a valid solution? Proper solution is below.

[cedar kiln]

Please don't occupy multiple help channels.

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[cedar kiln]

@unborn cobalt Has your question been resolved?

[ionic finch]

@unborn cobalt

[cedar kiln]

@unborn cobalt Has your question been resolved?

[unborn cobalt]

hi

@ionic finch ?

[odd snow]

0⁰ is an indeterminate form

[unborn cobalt]

I guess I will rephrase

is it solvable with just this and then plugging in 0

.close

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[covert island]

Can someone tell me where I went wrong here?

[crimson sedge]

The derivative of arcsin(x) is 1/sqrt(1-x^2)

Not x^2-1

[covert island]

Right

Arc secant is 1/xsqrt(x^2-1)

So I can’t use that either

[crimson sedge]

Do you know the trigonometric substitution technique?

[covert island]

Uhhhhh I forgot can you give me a small reminder

[crimson sedge]

Substituting the variable t with a suitable trigonometric function t=a*sin(theta)
as an example

[covert island]

Ohhh yes that’s right

So we’d use a sin theta

A tan theta

Or a sec theta

How do we tell which one to use

[cedar kiln]

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[crimson sedge]

Hello!

I have a depth image. I want to convert a pixel location to a translation vector. I have access to the pixel location (x-coordinate and y-coordinate) and the depth of the pixel in meters, aswell as the intrinsic camera matrix. How do I convert it to the translation vector?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

Hell nah

[dusty pasture]

react with an x to the bot message

[cedar kiln]

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[opal willow]

I've started by using the maclaurin expansion of ln(1+3x^2)

I know that x=1/2 gets me to a similar form, but it's not exactly that.

[copper plinth]

Take 1/4 common

Then try to figure out on you own

[opal willow]

What makes you think to take out 1/4 as a common factor?

like what is the thought process

[copper plinth]

Yeah. But my careless mistake. I think that's not gonna workout

Can you able to express it in more general form?

[opal willow]

Like as a summation?

[copper plinth]

Yep

[opal willow]

couldnt find the infinity symbol but hopefully u get it

and i know this

so by comparison i know that x=1/2

but im not sure what to do after that

[copper plinth]

I think it's confusing

Use more general series for ln

[opal willow]

what do you mean exactly?

like ln(1+x)?

[copper plinth]

$ln(1+x)=\sum_{n=1}^{\infty}(-1)^{n+1} \frac{x^n}{n}$

[wraith dagger]

kiddie_mano

[copper plinth]

Compare this with your series

[opal willow]

well instead of an n, we have an n+1 in the denominator

and x=3*(2^(-2))

[copper plinth]

Sry my bad I carelessly assume it's ln(x) instead of ln(x+1)

[copper plinth]

Use this

[opal willow]

ok, we just need to let x=1/2 and multiply everything by n/n+1

[copper plinth]

Can you about to find what is x in that series?

[opal willow]

if we let x=1/2, it gets us close to the series

[copper plinth]

That's obviously didn't give anywhere

[copper plinth]

Yeah but the prblm is the denominator

[opal willow]

so ur saying theres another value of x that can do the job?

[copper plinth]

Nope

X=1/2 that's confirm

[opal willow]

right, so we have to find a way to change ln(1+3x^2) to that summation

actually, its ln(7/4)

now that we let x=1/2

thats what ive been struggling with

so whats next?

[copper plinth]

Now you have change the series that exactly look likes this, even the denominator

But add and subtract something or multiply something

[opal willow]

thats the difficult part, im not really sure what to do

[copper plinth]

Finger out using the expanded series

[opal willow]

i have, ive looked at it for a while and cant seem to find the correct thing to multiply/add by

[copper plinth]

Look the expanded series?

You missing the 1 st term, right?

[opal willow]

my first term is 3/4

well i changed it to 3/2^2 to make it look more like the series

[copper plinth]

Nope 1 st term is 3/(2×4)

[opal willow]

oh ur talking about the Q

yea i am missing that

[copper plinth]

Yep

Change the question in the way that we can express as ln(1+3x²) and some additional terms

ln(1+3x²) is confusing?

[opal willow]

im not confused by anything

i just want to find a quick method to finding what to add/mulltiply/divide/subtract by to get the given form

is there nothing that i can apply here or it is just trying different combinations?

[copper plinth]

Look at the question... You just need to add 1 st term as 3/4, right?

And for remaining terms you have multiply each term with (-3/4)

Then you get ln(1+3x²) format, right?

You understand this much?

[opal willow]

oh

yeah

thats it

[copper plinth]

Do you get it now?

You can solve now, right?

[opal willow]

yeah, i just dont know how you realised so fast

thats what im asking

is there like a tricvk

what are u looking for exactly?

[copper plinth]

I did these kinda prblms in past.

[copper plinth]

What? I don't understand?

[opal willow]

like when you see two series' such as these two

what do u try look for

to solve it

[copper plinth]

I usually think it like a series.

Do you know partial sum?

[opal willow]

nope

[copper plinth]

But for this prblm. You the one who mentioned about ln(1+3x²), so I try to connect both ln(1+x) and you question. That's how I got the big picture

It's thanks to you

[opal willow]

its because its a part of another question where it asks us to find the expansion of ln(1+3x^2)

so they had to be linked somehow

[copper plinth]

It's basically instead of writing the series upto ∞ try to write upto nth term

[opal willow]

alright, then whats ur next step?

is it possible to just let my series, S, equal to a+bln(7/4) then just compare coefficients to find a and b?

[copper plinth]

Yeah. Somewhat math is all about connecting everything, that's why they try to give as much prblms as they could to train your brain with some particular method so that you can connect this in future

[copper plinth]

Then find for n+1 th partial series and go on. Eventually you end up with original question.

If you think deeply, it's basically finding limit sequence

My advise is do as much prblms as you can. Then you get the intuition behind it. But while solving it, enjoy it have fun with it

[opal willow]

okay cool, i think this is my best option

so i just cant apply some formula and get away with it, i actually have to try and think about it

[copper plinth]

So brain take it seriously, that means your subconscious brain will help you to tackle any prblms with ease

[copper plinth]

Yeah. Have fun with it.

[opal willow]

thanks

[copper plinth]

Any doubt?

[opal willow]

nope, makes sense now

[copper plinth]

Okie then it's time to close

[opal willow]

.close

[cedar kiln]

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[cedar kiln]

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[flat cypress]

I need to find the accumulation point/s.
I have found that sin repeats at 3k-2,3k-1 and 3k with 0, -sqrt(3)/2, +sqrt(3)/2 respectively. Cos repeats at 2k-1 and 2k with 1 and -1 respectively. I tried using sin repeat intervals and got nowhere and the same with using cos ones. I think I am approaching this in a wrong way and would like some pointers.

[cedar kiln]

@flat cypress Has your question been resolved?

[flat cypress]

<@&286206848099549185>

[coarse prism]

hi

idk if its gonna work

but you can draw a line and put this repeats in the line

and after that do the solution set of the values

[flat cypress]

I did, nothing useful came about, at least as far as I could see.

[coarse prism]

wait

cos is piK

and sin is K(7pi)/6

[flat cypress]

I am a bit confused. What do you mean to say?

[coarse prism]

the angle of the sin repeats 180 degrees with every K positive integre

cos*

sorry

the cos repeats 180 degrees

and the sin with 240 degrees

[flat cypress]

Yeah, I found the sequence for repetition of sin and cos, I just cannot use it since they don't match.

[coarse prism]

but you only need the sum of the cos and the sin right?

so you can do a solution set with all the possibilites of sum

[flat cypress]

I need to find accumulation point/s.

[coarse prism]

ok

[flat cypress]

Usually when I had cos and sin I needed to eliminate them via common repetition sequences. But these ones do not share it, so I am lost.

[coarse prism]

but they repeat themselves in the for K = 8

[coarse prism]

if you continue doing that they will repeat

[flat cypress]

Yeah, I know. But if I substitute for, let say 3k-2 my n I get indeterminate solutions.

The only idea I had was to substitute again but am unsure if that is allowed or not.

Something like this, although I do not think it is allowed.

[cedar kiln]

@flat cypress Has your question been resolved?

[flat cypress]

<@&286206848099549185>

I will be away for a couple of hours, not sure if I am supposed to close it or not in the mean time. I will leave it open.

[sonic thistle]

Hi me

[flat cypress]

https://tenor.com/view/kung-fu-panda-oogway-accidents-there-are-no-accidents-destiny-gif-16270886

[sonic thistle]

I agree with this

[cedar kiln]

@flat cypress Has your question been resolved?

[flat cypress]

<@&286206848099549185>

[cedar kiln]

@flat cypress Has your question been resolved?

[flat cypress]

Well I need sleep so I will close and maybe come back tomorrow

.close

[cedar kiln]

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[formal pasture]

did they round it wrong

shoudlnt it be 1.1x10^3?

[cosmic steppe]

,w 125 * cos(40 deg) * 12

[wraith dagger]

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Requested by Umbraleviathan#3607

[cosmic steppe]

Uh no

One Newton-meter is one Joule

[formal pasture]

like this

[cosmic steppe]

If you round it to significant figures, 1149 Nm -> 1.15 * 10^3 J

[formal pasture]

buut

how is it 3

[cosmic steppe]

Because the leading digit is in the thousands

10^3 = 1000

So 11.5 * 10^3 = 1150

[formal pasture]

im confused

[cosmic steppe]

What about it is confusing

The leading digit is in the thousands

[formal pasture]

wdym by leading

[cosmic steppe]

Highest digit

Like for example the leading digit in 706 is the hundreds

[formal pasture]

yea

[cosmic steppe]

Where it's 7.06 * 10^2

[formal pasture]

yea

okkty

.close

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[plush coyote]

I dont understand how to do these 2 problems

[plush coyote]

Its basic trigonometry so no herons law or any of that just sohcahtoa sine law and metric relations

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[calm flicker]

need to find area of shaded

(area of composite chapes)

[frail thistle]

start by decomposing these into separate shapes

both of these are rectangles with sections removed

you find the area of the rectangle and subtract the area of the removed sections to find the area of the shape

[calm flicker]

@frail thistle i know that but how on earth am i suppost to find the length of the tiny sides length

[frail thistle]

do yk what the little tick notations mean

[calm flicker]

no bro

test tmr teacher didnt teach anything @frail thistle

[frail thistle]

okay so

that means the sides are equal

all 5 sides on the bottom row and middle row are equal

[calm flicker]

aight

but how do i find the length

[frail thistle]

and since the top is 5, each of the bottom ones must be 1/5th the total width or 1

[calm flicker]

thank u man

i get it

and wb the bottom question

[frail thistle]

uh

well

the diameter of the circle is equal to the height of the rectangle

for both circles

cuz the circles r inscribed

[calm flicker]

would it be

π(3) squared + π(1.5) squared

[frail thistle]

uhh

well

the diameter is 3

[calm flicker]

ye

[frail thistle]

and the radius is half that

so it would be 1.5 as the radius for both of them

[calm flicker]

1.5

ah

[frail thistle]

and since one of them is only a semicircle

you divide the overall area of the circle by 2

[calm flicker]

ight ight

i get it

and subtract that by 18?

cuz 6x3 for the rectangle

[frail thistle]

you subtract the areas of the circle from the rectangle, because youre trying to find the area excluding the circles

[calm flicker]

so id subtract it from 18, correct?

@frail thistle

[frail thistle]

yea

[calm flicker]

ty bro

i appreciate u a lot

[cedar kiln]

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[rare wadi]

can someone explain it to me?
"Prove linearity of a given transformations of vector spaces"

[cedar kiln]

@rare wadi Has your question been resolved?

[rare wadi]

<@&286206848099549185>

[storm mural]

what are the linearity conditions

[rare wadi]

L(a + b) = L(a) + L(b)
L(ax) = aL(x)

[storm mural]

yes

[rare wadi]

how can i start solving this?

[cerulean sail]

Show these to be true: given a $(x_{1}, y_{1}, z_{1})$ and $(x_{2}, y_{2}, z_{2})$, show that $L( (x_{1}, y_{1}, z_{1}) + (x_{2}, y_{2}, z_{2}) ) = L( x_{1}, y_{1}, z_{1}) + L(x_{2}, y_{2}, z_{2})$ and that given some constant $\alpha$, that $L(\alpha(x, y, z) ) = \alpha L(x, y, z)$

[wraith dagger]

@cerulean sail

[cedar kiln]

@rare wadi Has your question been resolved?

[cedar kiln]

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[barren saddle]

I’m trying to figure out if this is possible. It was on an assignment I turned in and I am trying to remember the problem but this is all I remember. Basically it was about two cars. Car 1 had the equation f(t)=40(0.90)^t and car 2 had a graph that stated that car 2 reached $10,000 in 10 years. And the question asks how many years car 1 would take for it to cost $10000. Let me know if this makes any sense.

[cedar kiln]

@barren saddle Has your question been resolved?

[barren saddle]

<@&286206848099549185>

[rain vine]

not much information

I already tried the question but stuck in the middle way since nothing can be cancelled

[barren saddle]

I see it’s just all I remember thanks anyways.

.close

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[crimson sedge]

What are some limitations of the surge function model in medicinal doses?

[crimson sedge]

f(x)=Axe^-bx

(surge function)

[devout star]

wdym

[hazy sparrow]

The surge function model has several limitations in medicinal doses:

Limited applicability: The surge function model is suitable only for drugs that follow a one-compartment pharmacokinetic model with first-order elimination kinetics. Many drugs have complex pharmacokinetic profiles that cannot be accurately modeled using this function.

Lack of flexibility: The surge function has a fixed shape, and it cannot accommodate deviations from this shape that may occur due to factors such as drug interactions or changes in the patient's physiological state.

Inability to account for individual variability: The surge function assumes that all patients will respond to a drug in the same way. However, individual variability in factors such as metabolism, body weight, and age can significantly affect drug response.

Limited predictive power: The surge function can provide an estimate of drug concentrations in the body, but it cannot predict the actual clinical effects of the drug on the patient. The clinical response to a drug depends on many factors beyond its concentration, such as the drug's pharmacodynamics and the patient's underlying medical conditions.

Limited utility in dose optimization: The surge function can be useful in determining initial dosing regimens, but it may not be sufficient for optimizing dosing over time. Factors such as drug accumulation, tolerance, and drug interactions can significantly affect the optimal dose and dosing interval for a patient.

[crimson sedge]

great thanks but

wai yes

thanks

@hazy sparrow

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[cedar kiln]

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[distant halo]

hello, i need help solving this
i dont know what to do nor how to do it

[cedar kiln]

@distant halo Has your question been resolved?

[distant halo]

<@&286206848099549185>

.close

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[dim flint]

Anyone know this notation?

What's it's called and how to use it

[buoyant perch]

which bit

[storm mural]

union from n = 0 to 10 of {n}

{0} U {1} U {2} ... {10}

just like sum

[dim flint]

Is U logic notation?

Or does it do something

[storm mural]

set theory

#❓how-to-get-help

[storm mural]

wdym

[buoyant perch]

go to an empty channel in math help and ask there

[storm mural]

it gets the smallest set that includes all the elements of both sets being united

[dim flint]

Oooh ok

[vague rapids]

#❓how-to-get-help

[dim flint]

I got you

[buoyant perch]

up 1 section on the channels

[dim flint]

Thank you

.close

[cedar kiln]

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[radiant topaz]

#❓how-to-get-help

[cedar kiln]

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[sharp grove]

Can someone help me w vectors that r 3D

[sharp grove]

IK how to do stuff w 2D vectors but idk 3D

[buoyant perch]

post the question

[sharp grove]

Yea gimme a sec

[radiant topaz]

Yeah

[sharp grove]

Like this

How do u find the equation of a plane?

And r planes only w 3D?

[buoyant perch]

what do you know so far

dot product cross product?

[sharp grove]

Ik 2D vectors

Yea ik those 2

[buoyant perch]

which question is the one you are struggling with

[sharp grove]

WAIR lemme start w this one

#5

When it doesn’t have a 3rd dimension, would u js write it as 0?

[buoyant perch]

yes

[sharp grove]

Ohh ok

So based on my work was I doing it right?

[buoyant perch]

3i + 0j + k

yes

[sharp grove]

Yay

[wraith dagger]

fäf

[sharp grove]

Ah ok

Ok so I get that part

[tardy vale]

how did you get text outside the paper what

[sharp grove]

Oh LOLL it was another wkst under 😭😭

[radiant topaz]

Shadow exists

[sharp grove]

Then another question asked to find the direction angles for vector v=2i-3j+k

How do I do that lol

[buoyant perch]

should just be basic trig

[radiant topaz]

Direction cosines

Find them first

[buoyant perch]

oh yeah thats easier

[sharp grove]

So

How do I do that 💀

[radiant topaz]

The direction cosines are equivalent to component of unit vector in some direction

[sharp grove]

Alr so find unit vector first then inverse cos for each ?

[radiant topaz]

Yes

[sharp grove]

Ok so when I answer the question do I have to specify which angle goes with whatever value?

Like 57.68° i, 143.3° j, 74.5° k

Or smth lkke that

[radiant topaz]

Not using I,j,k

Give a notation to angle with respect to each axis

[wraith dagger]

fäf

[sharp grove]

Ohh

Okok

Ty

[radiant topaz]

You're welcome

[sharp grove]

Oh wait I have another question

Lkke 2 lol

First #8 tho

[radiant topaz]

You know how to get directional vector from a point to another?

[sharp grove]

I’m not sure

Would it not just be the points subtracted from one another?

[radiant topaz]

Yes

[wraith dagger]

fäf

[sharp grove]

Ohh ok

So for 8 the directional would be <3, 1, -9>

[radiant topaz]

Ok

[sharp grove]

?

[radiant topaz]

Okay

[sharp grove]

Is that right lol

<@&286206848099549185>

Sry for ping

[radiant topaz]

Yes

[sharp grove]

Okay ty

Is that it?

[radiant topaz]

No

[sharp grove]

Oh

[radiant topaz]

.

[sharp grove]

Huh

What does each letter represent I’m confused

[radiant topaz]

a and b are position vectors

[sharp grove]

Ohh

[radiant topaz]

The ones given in question

[sharp grove]

Oh

Theh what’s the upside down y thjng

[cedar kiln]

@sharp grove Has your question been resolved?

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[crimson sedge]

Need help w/ this equation my tangent lines are weird when i graph them on desmos 😭

[crimson sedge]

so the p.o.t I got is (-5, +/- 2.25)

[radiant topaz]

Find the tangents

[crimson sedge]

i did

but mine look weird i think i mightbe did it wrong

[vagrant elbow]

There's a general tangent equation for hyperbolas

[crimson sedge]

yes

x^2/a^2 - y^2/b^2 = r^2

[vagrant elbow]

$y = mx \pm \sqrt{a^2m^2 - b^2}$

[wraith dagger]

NEONPerseus

[vagrant elbow]

Was it this

[crimson sedge]

oh sorry

[vagrant elbow]

The tangent to a hyperbola not the hyperbola

[rain vine]

@vagrant elbow what's this called how do we write this?

$ y = a^2

[radiant topaz]

Guess the pm is for mx

[radiant topaz]

Latex

[vagrant elbow]

It's called LaTeX #latex-help

[rain vine]

oh okay

[vagrant elbow]

Was it? I don't remember really

[crimson sedge]

my tangent line of equation is y+/- 2.25 = +/-1.25(x+5)

[vagrant elbow]

Let me have a look

[crimson sedge]

because point of tangency is (-5, +/- 2.25)

and slope is (+/- 1.25)

[vagrant elbow]

The pm seems to be for the constant term

[radiant topaz]

Yeah right

[crimson sedge]

but my tangent line this

it aint right

[vagrant elbow]

,w equation of tangent to 9x^2 - 16y^2 = 144 at x = -5

[wraith dagger]

Results provided by WolframAlpha

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

Requested by NEONPerseus#2128

[crimson sedge]

wait what

[vagrant elbow]

[crimson sedge]

i got 9x/16y as my general derivative

[buoyant perch]

probably dont just post the answer

[vagrant elbow]

Was just verifying lol

We still don't know how to arrive at the answer

OP is clearly motivated to do it

[vagrant elbow]

Seems correct

[crimson sedge]

right

hold on

omygod

i think i know what i did wrong

yes omygod

I just got my sign mixed up

[vagrant elbow]

Alright cool

[crimson sedge]

😻

ty

.close

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[crimson sedge]

What's ∞ + ∞ = ??

[buoyant perch]

what is this question for

it doesnt really make sense

there is no ∞

[crimson sedge]

this is indeterminate form?

[crimson sedge]

well its infinity again ig? we usually don’t just use infinity we use limits.

[crimson sedge]

Universe .... Something on a quantum scale

[crimson sedge]

Then what if we subtract infinity from infinity

[buoyant perch]

that also means nothing

[crimson sedge]

idk

[buoyant perch]

it depends on the infinities

[crimson sedge]

infinity is just a concept its not defined as a number

[buoyant perch]

also infinity is not a number

[crimson sedge]

ya

[crimson sedge]

That's ummm 🤔

i think vsauce said it himself

iirc

even my calc teacher said so

[crimson sedge]

Do you know quantum tunneling.... If yes then I guess infinity is something like a unreachable limit

[crimson sedge]

Can you share video link

[vagrant elbow]

That's Infinity

[vagrant elbow]

Depends on the context

Is this regarding limits

[crimson sedge]

Then I need some explanation for ramanujan paradox

https://www.youtube.com/watch?v=SrU9YDoXE88&ab_channel=Vsauce

idk if this relates but I just thought of this vsauce video when u mentioned infinities

[vagrant elbow]

$\sum_{k = 1}^{\infty} k = -\frac{1}{12}$

[wraith dagger]

NEONPerseus

[vagrant elbow]

This?

[crimson sedge]

Yeh this

[vagrant elbow]

I think there's a BriTheMathGuy video on it

[crimson sedge]

This is a trick right ?

Like logically it's infinity

[vagrant elbow]

Yes

It comes down to manipulating sequences

[crimson sedge]

I'll make sure to watch it

[vagrant elbow]

And how legal these manipulations are is up for debate

It doesn't break rules afaik but it relies on axioms (that may not be acceptable to all)

[crimson sedge]

Yeh but many questions of sequence and series are solved by this manipulation

[vagrant elbow]

Yes I'm aware, it's why it's famous

[crimson sedge]

And if this type of manipulation works for other then why not for this ....

It's just frustrating

[vagrant elbow]

It comes down to quirks in infinite summation

Like the legality of the distributive property over infinite summation

Most people do it without a thought though

[crimson sedge]

Ohh

Anyways I think I am wasting others time ... Lemmi close

.close

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[flat harbor]

simplify the expression:
log(x) + log(1/x)

[flat harbor]

wait isnt that just 1

bc x * 1/x is 1

[vagrant elbow]

It's log 1

[flat harbor]

thats waht i meant

thanks mate

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[mint mango]

log a of 1 is always 0

[flat harbor]

true

.reopen

[cedar kiln]

✅

[flat harbor]

simplify this tho

$\frac{\log(xy)}{\log(x)}$

[wraith dagger]

StopTheKap

[vagrant elbow]

$\frac{\log xy}{\log x}$

[wraith dagger]

NEONPerseus

[vagrant elbow]

Split

[flat harbor]

how does one simplify this

[vagrant elbow]

The upper log

[flat harbor]

into logx + logy

how does that help tho

[mint mango]

1 + logy/logx

[flat harbor]

oh ok

[vagrant elbow]

I mean you can directly use base change theorem I suppose

[flat harbor]

nah its alright

leave it that way

thanks mate

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[coral plover]

Can someone help me understand the monotony of graphs and functions?

[coral plover]

As I understand it a graph can be said to be increasing if the gradient is positive, and decreasing if the gradient is negative, this I understand

But i'm getting questions in which I'm asked if the entire function is increasing or decreasing, which doesn't make sense to me

f(x) = x^3 + x + 5

for example

and all i'm told is to find out whether the function is increasing or decreasing

shouldn't I be asked to find out whether its increasing or decreasing at a certain point?

how can I find out whether a function is increasing or decreasing just from its equation?

Some functions increase in some places and decrease in others

[meager jungle]

find f'

[crimson delta]

well the function could be increasing or decreasing everywhere

or maybe on two intervals

so find the gradient and check where it is positive and where it is negative

[coral plover]

I have found f'. My question lies mainly in how this question is asking me to categorize these functions

apparently i should be able to say

"the function f(x) is increasing" - end of statement

not "increasing at x = c"

[meager jungle]

if you found f' you should be able to answer the question

[coral plover]

f'(x) = 3x^2 + 1

[crimson delta]

"function is increasing" means "function is increasing at every point"

[meager jungle]

that function is always positive

[coral plover]

"neither" is also an option

when would i say that

[crimson delta]

eg f(x)=x^2 is not increasing or decreasing on all of R. only on parts of it

or f(x)=sin x. stuff like that

[coral plover]

so that's when you would say neither

okay

apparently this function is increasing

is this because you get a positive value for f'(x) no matter what x val you put in

[crimson delta]

yes

[coral plover]

so how would you do this "check" mathematically?

[crimson delta]

x^2>=0

[coral plover]

cuz i got to that conclusion by imagining a parabola that never goes below y = 0

[crimson delta]

and then you are scaling that and adding 1

to get >0

[meager jungle]

you should be able to draw a quad if youre doing calculus

[coral plover]

I am able to draw one, but this parabola was quite intuitive to me so imagining that it never dips below y = 0 was simple enough

[meager jungle]

ok then problem solved

[coral plover]

but how would I check if the derivative of this goes below 0 for example:

[meager jungle]

find f' first

[crimson delta]

well for starters try calculating the derivative

[coral plover]

yes I have

[crimson delta]

then use that e^x >0

[meager jungle]

it doesnt

[coral plover]

.close

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[wraith dagger]

hwacc

[meager jungle]

hm

dunno

[cedar kiln]

@unborn dagger Has your question been resolved?

[meager jungle]

my best guess is that the integral was supposed to be F(x)

[astral bay]

yeah with the question as written there the fact that F' is the derivative of F is completely irrelevant because F isn't mentioned anywhere else, so there's probably a typo somewhere

since knowing the derivative of a function everywhere isn't sufficient to get its value at any one point (you can always add a constant) i'm guessing they meant that F(x) = \int_0^x e^{-t^2} dt

[meager jungle]

its a definite integral

so constants dont matter

[cedar kiln]

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[languid pine]

can someone pls confirm

does this function have a critical point at x=0

so is this function not differentiable at x=0

[tropic oxide]

critical point does not imply non-differentiable

[copper plinth]

Do you know what is critical point

[tropic oxide]

the derivative of 0.3x^2 is 0.6x, including at x=0, where the derivative equals 0

[languid pine]

bruh

this is what schools teaching me

[opaque root]

a implies b doesn't mean b implies a

[tropic oxide]

bruh

[languid pine]

my teachers teaching me wrong ig

[buoyant latch]

Under that definition do you think x=0 is a critical point?

[languid pine]

no

clearly it is differentiable at that point

[copper plinth]

But clearly that statement doesn't said if at a point function is differentiable then it's not critical point

[languid pine]

based on my teachers definition

x=0 is not a critical point

based on what ive just learnt from this convo

it is

[copper plinth]

Clearly this photo doesn't mentioned it's a definition

[languid pine]

yeah its a definition she said to refer to when answering the question

[copper plinth]

According to wiki

[languid pine]

so this point is a critical point bc the derivative is 0

[copper plinth]

Yeah

[languid pine]

so i look at critical points based on both criteria

ok thank you

[copper plinth]

Talk to your teacher about it

[languid pine]

yeah im trying to rn

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[tropic oxide]

!status

[cedar kiln]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[full karma]

1

step 1

wait actually step 2

[steel heart]

!show

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[full karma]

i used trig identity sinh(x)=(e^x-e^-x)/2 and substituted it

[tropic oxide]

that's not a trig identity that's just the defn of sinh

[full karma]

sorry, yes that is correct

[tropic oxide]

so now you have transformed your expression into $\frac{\frac12(x^3+x)(x^4-x^{-4})}{\frac12(x^4+1)(x-x^{-1})}$

[wraith dagger]

Ann

[tropic oxide]

note at this point that this is just an algebraic expression with no trig involved

perhaps stating this explicitly will help you

[full karma]

ahh ok thanks

.close

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[unique tiger]

is there any calculator to check my answers ? i need to to solve for the coefficents and not the X

[cedar kiln]

@unique tiger Has your question been resolved?

[copper plinth]

what does the question even mean?

[soft cloak]

Translating :
Let V = {real polynomials of degree ≤ 3} and U generated by p₁, p₂, p₃ as given. For each given p, determine whether it lies in U. If it does, write p as a combination of the pᵢ and give the coefficient that is asked.

For the first question, p = 2X²+4X-6 and they must determine a₁, the coefficient of p₁.

[soft cloak]

How did you arrive at the answer of -2 ?

[cedar kiln]

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[unique tiger]

.reopen

[cedar kiln]

✅

[unique tiger]

i am not sure if that is even correct

i just tried counting in my head

i am sorry i was on a deadline and had to submit it

[soft cloak]

i suggest you just try on paper

[unique tiger]

what should i write

could you show me one and i will do the rest ?

[soft cloak]

try to write p as the combination of the pᵢ, that will give you an equality of polynomials with the aᵢ in the coefficients

two equal polynomials must have the same coefficients, so that turns into a system of equations

for example

For p = 2X²+4X-6, let's try to write p = a₁p₁+a₂p₂+a₃p₃. The X³ coefficient of p is 0, and the X³ coefficient of the combination on the right is a₁+a₂+a₃, correct ?

Therefore if the aᵢ exist, these two must be equal, i.e a₁+a₂+a₃ = 0.

Do this for each term and you'll get a system of 4 equations in 3 variables. That might not always have a solution, so you need to check that.

[unique tiger]

oh i see

i am gonna try to do one on paper

[unique tiger]

so i multiplie also the coefficents of the x's with the a's right ?

i got the answer 2

[soft cloak]

-2a₂ = 6 means a₂ = -3, not 3

[unique tiger]

oh whoops

but is the method correct ?

[soft cloak]

yes

[unique tiger]

okay thank you very much ❤️

vielen dank

[soft cloak]

bitte

[cedar kiln]

@unique tiger Has your question been resolved?

[cedar kiln]

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[full karma]

hi

[full karma]

im stuck on a question

ive gotten to here $\frac{\frac12(x^3+x)(x^4-x^{-4})}{\frac12(x^4+1)(x-x^{-1})}$

[wraith dagger]

spazdell

[full karma]

would it be $\frac{\frac{1}{2}\left(x^7-x^{-1}+x^5-x^{-3}\right)}{\frac{1}{2}\left(x^5-x^3+x-x^{-1}\right):}$

[wraith dagger]

spazdell

spazdell

[full karma]

or am i missing something

$\frac{x^7-x^{-3}}{-x^3+x}$

[wraith dagger]

spazdell

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[eternal knot]

Here is what I was given regarding cooling problems

nevermind I think i got it

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[grand storm]

how does this integration work?

[cedar kiln]

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[radiant topaz]

By parts

[grand storm]

hm ok

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[crimson sedge]

I need help with this

In the public debate in Denmark, there is a lot of focus on the transport sector's emissions of CO2, including the effect of passenger cars on emissions. There are e.g. has been set a target of 1 million electric cars in the year 2030. Statistics Denmark calculates the sales of new cars in Denmark on a monthly basis. The figures are calculated according to the vehicle's fuel (e.g. petrol, diesel and electricity).
The monthly figures for the sale of new cars with the fuels petrol, diesel and electricity since January 2018 can be found in the data file.
a) Make an analysis of the development of sales of new cars in Denmark in the period from January 2018 to August 2022 based on the data material.

The analysis must include:
• Graphical presentations
• Calculations on developments in the sale of cars calculated both in total and on fuels
• Projections of the developments towards 2030 in total and on fuel
• Conclusions on various graphical presentations and calculations

In the analysis, index numbers, curve diagrams, linear and exponential developments, regression analyzes etc. can be used.

[crimson sedge]

I can provide the Excel file too

Here is the Excel file

[granite knoll]

this is a whole project basically

[crimson sedge]

My assignment has 4 questions and I answered 3 but this 4th one is very hard for me

[granite knoll]

what 4th question?

[crimson sedge]

I mean this one I post here

Posted*

[granite knoll]

"make an analysis" isn't a question like most of the ones posted here. it's a whole "project", you need to go through the analysis

[crimson sedge]

I did but it is hard

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[ornate ridge]

Translated: Solve the equation, give an exact answer.

[gritty viper]

(1,2√x) is not a number and cannot be added and subtracted from numbers

[cedar kiln]

@ornate ridge Has your question been resolved?

[ornate ridge]

I assume it to be 1.2*sqrt(x)

And not a coordinate

[gritty viper]

ah fair enough, though that doesn't explain why it's in parentheses

[ornate ridge]

Also felt that was strange

[gritty viper]

first step I'd do is what's log(100)

idk I'd be surprised if this has an exact answer though

[ornate ridge]

Oh, well the question was wrongly typed in

(the actual question)

This explains the parenthesis

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[hallow pike]

To find the sum of an infinite geometric series we need to use a formula but the common ratio r should be less than 1
Why is that?

[tropic oxide]

the series diverges otherwise.

[livid hound]

consider the full formula for the sum of n terms in a geometric serires

[tropic oxide]

also it's |r| < 1 rather than r < 1

[livid hound]

and see what happens when |r| > 1
and take the limit as n→inf

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@hallow pike Has your question been resolved?

[hallow pike]

Ohh okay

Thank you

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[haughty walrus]

I have this classwork I'm unable to solve, we weren't taught how to do this. Can someone explain to me how to solve it step-by-step?

[iron jackal]

It uses circle theroems, are you aware of any of these?

[haughty walrus]

Absolutely not, that wasn't even in the book. 😭

[iron jackal]

I'm ngl they are just a pain and I just had to remeber them. It is worth practising them cuz they like putting them in tests

[haughty walrus]

Oh hang on I'm aware of them, but I don't know how to solve it. I'm currently given the formula (a+b)a=(c+d)c. I think the answer turned into a polynomial and I'm stuck after that.

[iron jackal]

What polynomial did you get?

[haughty walrus]

5x^2-5x-40

[iron jackal]

= ...?

[haughty walrus]

0

[iron jackal]

You can use the quadratic formula to solve for x then

[haughty walrus]

I forgot about that thank you so much!

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[vital cargo]

why do all pentagons add upto 540 degrees

[vague rapids]

(n-2)*180

[vital cargo]

thanks

gigachad

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[jade stag]

Hey. calculus problem. is this correct?

[jade stag]

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[primal robin]

If anyone here is familiar with twitch's prediction system, it will be very helpful.

Suppose we have a betting system as such: There is a pool of total money. There are two options to bet. For each option, there is a return ratio - a fraction that is the factor that determines how much money you will gain back. So if the return ratio is 2, you will get twice as much money as you put in. Now, the return ratio is determined by the percentage of your bet from of the total money. So, if one option was bet with 50% of the total money, the return rate of that option will be 2. If the option was bet with very small % of the total money, the return rate will be very high as the option is risky.

[fair geyser]

it's kelly criterion

precisely this

[primal robin]

Yes I have heard this term, thanks for the clarification. What I want is to find the formula that gives me the return ratio given the opposite return ratio. So if I put 2, it will give 2, if i put a large number it will be closer to 1, etc etc.

[fair geyser]

1+1/(x−1)

= x/(x−1)

[primal robin]

Hmm, alright, this seems right.

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[muted bear]

what in the

[tight oracle]

I'm not sure how to differentiate since there's theta and w

[muted bear]

,rotate cw 15

,rotate 15

[muted bear]

sure

differentiate with respect to time

[tight oracle]

okay I'm gonna try that

I got this

but Idk how I can use that to find the critical points

The way I see it:

1. I need to represent the derivative where I can disregard w.
2. I need to find all critical points for the function.
3. I need to reject critical points outside of the restricted domain
4. I need to determine absolute maximum and minimum for the closed interval.
5. I need to evaluate the function at max and min to answer with the max and min velocities.

Is anyone able to help with 1?

I'm stuck at how to get to the critical points, I feel pretty confident with finding critical points with only 1 variable, differentiating trig functions generally, finding absolute max and min for an interval.

[severe bison]

differentiate wrt to theta

@tight oracle

[tight oracle]

doesn't that give me the same issue but now I have dw/dθ instead of dw/dt?

implicit differentiation is messing me up

[severe bison]

Why are differentiating implicitly?

w is constant

[tight oracle]

I have no idea

so it remains there

just a # that idk

[severe bison]

Yes just the trig thing you play with

Then find critical points at usual you will have infinite solns for theta choose between the given range

[tight oracle]

so I got da/dθ=-(w^2)(sinx+sin2x)

[severe bison]

Equate it to zero

find critical points

[tight oracle]

then critical points of 0, pi, 2pi/3, 4pi/3, 2pi

since crit points include the interval bounds then I would just solve for a at each point, then determine max and min?

assuming my derivative and crit points are correct

[severe bison]

Yes now these are the points of maxima or minima check it by plugging in the real equation

[cedar kiln]

@tight oracle Has your question been resolved?

[frail thistle]

hey we have the same pfp

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[ionic finch]

I'm trying to improve my arithmetic skills.

let me say, how I approach this problem,

better ill post a picture

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[solid mortar]

6+x-x²
how do you get the points where this formula hits the 0 on the x axis?

[ionic finch]

also know as roots of polynomial

we have first factor the given polynomial

given $-x²+x+6$

[wraith dagger]

Dubleyou

[ionic finch]

we can split the middle term

$-x²+3x-2x+6$

[wraith dagger]

Dubleyou

[ionic finch]

$-x(x-3)-2(x-3)=(x-3)(-x-2)$

setting $(x-3)(-x-2)=0$ gives us the roots of where it touches x-axis

ie,$x-3=0$ or $-x-2=0$

which is x=-3 or x=-2

,w plot -x²+x+6

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Dubleyou#6412

[solid mortar]

oh my this seems complicated, ty ill try to get it

[wraith dagger]

Dubleyou

Dubleyou

Dubleyou

[ionic finch]

which is x=3 or x=-2

[cedar kiln]

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[foggy merlin]

is it even possible

B isnt a 3x3 matrix

[dire geode]

you're getting trolled

[exotic tusk]

i suppose C/2 is to divide each number in C by two.
i already have 2A and 3B, how im supposed to fubd 2b +3b if theyre different sizes

really?

oh i got really confused for a sec, thanks

can i do 2A + C/2 at least

or i just send it like that

[dire geode]

yes you can

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[loud falcon]

Hello

[cedar kiln]

Please don't occupy multiple help channels.

[royal loom]

@loud falcon use this one for your question

[loud falcon]

Thank you