help-26

[real blaze]

-35 or 35?

[cursive patrol]

-35, -7, -5, -1, 1, 5, 7, 35

[real blaze]

-5,+7 or +7-5

Yes

X=5 satifies

[mossy tree]

no

[real blaze]

Why not?

[knotty ledge]

Odd degree polys will have atleast one real root if that's what you mean

[real blaze]

So it can be more than 3 ?

[knotty ledge]

Not for a cubic no

[mossy tree]

can cut more than once

for example: f(x) = (x-1)(x-2)(x-3)

So f(x) is third degree

[real blaze]

I meant in our quation we have no x^2 term

[mossy tree]

But we can clearly observe that it cuts in three places

No it can't

If that were the case it would have to be something of degree 4 or higher

[real blaze]

This

[mossy tree]

understand, I didn't think about it

so the question you asked:

Does a cubic function that does not contain an x² term intersect the x-axis three times?

[real blaze]

Yes yes

I meant it is possible or not?

I am interested to know about what kind of roots will be there

[mossy tree]

so

I looked into it a bit

can cut three times again

ax³+cx = x(ax²+c)

x = 0 or x = ±√(-c/a)

[real blaze]

I see, what you found?

[mossy tree]

There can be 3 roots if -c/a > 0

[real blaze]

Could you make any equation with it?

[mossy tree]

yes

like what

i can say x³-5x

maybe

[real blaze]

So if we look at descart rule

3 real roots ☺️👌

Let's work out with our main problem with Descartes it represents (3 real roots, 1 real 2 complex roots)

[mossy tree]

in which situation?

@real blaze

[real blaze]

This one

[topaz sinew]

@real blaze Has your question been resolved?

[real blaze]

.close

[topaz sinew]

Channel closed

Closed by @real blaze

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[topaz sinew]

@sonic pawn Has your question been resolved?

[topaz sinew]

@sonic pawn Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[toxic zealot]

I need to show $a_n = 1+ 1/a_{n-1}$ converges to the golden ratio

[thorny flame]

Junojuno

[chilly walrus]

multiply both sides by a_{n-1}

and recall that $\phi^2 = \phi + 1$

[thorny flame]

artemetra

[last parcel]

$an=1+1

$an=1+1$

[thorny flame]

brahim3579

[last parcel]

iam professional

[topaz sinew]

@toxic zealot Has your question been resolved?

[toxic zealot]

I need to prove convergence

Formally

[topaz sinew]

@toxic zealot Has your question been resolved?

[mossy tree]

@toxic zealot What exactly is the problem?

x² = x+1, then x = golden ratio

we know that already

so what is the problem?

[toxic zealot]

,close

.close

[topaz sinew]

Channel closed

Closed by @toxic zealot

Use .reopen if this was a mistake.

[hallow depot]

lol

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crisp raptor]

I crafted myself a problem to get better at integrating in the R^2 plane with double integrals, I want to calculate the Area A with double integrals

[crisp raptor]

$\int_{x_1}^{x_2} dx\int_{y_1}^{y_2} dy$

[thorny flame]

tobi

[crisp raptor]

where y_1 and y_2 are functions of x of x_1 and x_2 are functions of y how can would I try solving this problem?

I also calculated all the functions that represent the line segments if that helps

[supple mist]

i would not use integration.

💀

[crisp raptor]

why? it has to work and I probably get a lot of insight in to how to solve similar problems

[ancient falcon]

How do you get better at integrating without using integration?

ed was solid 5 minutes ago, but... damn, people can't read today

[supple mist]

but wouldn’t you craft a better problem

instead of a damn triangle

which there a countless better methods to find areas of

[ancient falcon]

Plus, I'm really spicy today 😉

[supple mist]

@crisp raptor i have problem sets for finding areas in R^2

i can give you a few problems

that are integration focussed btw

[crisp raptor]

what is wrong with this problem

[supple mist]

fine

if you insist

integrate from the green line to the red line from 1 to 1.5

and then green line to blue line from 1.5 to 2.5

[crisp raptor]

I could integrate von y=1 to y=2.5 (green line) and then subtract 1 to 2.5 from the red one right? and so on then I just repeat that untill im done

would that work

[crisp raptor]

I dont actually wanna write all of this down I just want to understand how I would do it

[supple mist]

y wise?

w/ respect to y you should be doing 1 to 3

intersection is at y=3

but yes that would work

[crisp raptor]

ops

[supple mist]

this isn't double integration btw

you don't need a double integral to solve this

[distant vine]

technically you can with a double integral if you integrate dxdy on the domain of the triangle

but pls dont

[supple mist]

yeah but why.

💀

[distant vine]

even a single integral is pushing it for calculating the area of a triangle

[supple mist]

i already said this

[crisp raptor]

$\int_{A} d\lambda^2$

[supple mist]

tobi insisted tho

[thorny flame]

tobi

[supple mist]

to do it with integration

i'll just write what it would be

[crisp raptor]

yes the first integral would just give me the function that im integrating (f,g and h right)

[supple mist]

yeha i think thats right

[thorny flame]

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

[crisp raptor]

lets say I want to integrate this

$\int_{A} d\lambda^2 y^2 x^2$

[thorny flame]

tobi

[crisp raptor]

then I have to do it like this

[supple mist]

oh

[crisp raptor]

thats a reason why I want to learn this

[supple mist]

i see

[crisp raptor]

I can have a whole function f(x,y) where I integrate over the domain of the triangle

[supple mist]

yes

you sholud have led with that

c

[crisp raptor]

because we integrate the 1 function ofc its the area

[supple mist]

$\int_1^{\frac 32}\int_{\frac43x-\frac13}^{6x-5} x^2y^2,dy, dx$

[thorny flame]

ed

[supple mist]

this would be one part

then you would do between the yellow and green line

similarl

y

[crisp raptor]

I understand the x integral can you please explain why you choose 4/3x-1/3 on the bottom and 6x-5 on the top

[supple mist]

thats the green line

6x-5 is the red line

[crisp raptor]

would this be correct?

are we integrating the purple part

[supple mist]

yes

we ar

[supple mist]

this integral is the purple part

[crisp raptor]

is this true in general that if I want to integrate an area in R^2 between 2 functions, that the upper and lower bound are those functions? and then its the area between those graphs?

it should be right?

[supple mist]

yes

it is true

the signed area

thats why red is the upper bound

[crisp raptor]

because then we only have 2 different integrals?

[supple mist]

wdym?

[crisp raptor]

wait I dont wanna integrate from x=1 to x=4 here because then I would have to solve g(x) and f(x) for x right?

that would also work

or what is the reason why you did not do that

[supple mist]

because that would be a piecewise function

so we just take two double integrals

[crisp raptor]

,w integrate from 1 to 3/2 (6x-5-(4/3x-1/3))

,w integrate from 3/2 to 4 (2/5x+17/5-(4/3x-1/3))

[thorny flame]

Results provided by WolframAlpha

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

Requested by tobi_012345

Results provided by WolframAlpha

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

Requested by tobi_012345

[crisp raptor]

I dont get the correct result with this method

im confused

[crisp raptor]

what is that function

for purple

[cyan mesa]

-3/4(x-1.5)+4

The length of the purple line is actually 1.4

[crisp raptor]

oh

[cyan mesa]

So the area should be 3.5

[crisp raptor]

thanks!!

[cyan mesa]

[crisp raptor]

then everything works

[crisp raptor]

how did you calculate it to be 1.4

[cyan mesa]

Distance

sqrt((x2-x1)^2+ ….))

[crisp raptor]

ah the norm of the vector in R^2 ?

[cyan mesa]

Err no idea honestly

[crisp raptor]

it just gives you the length

and its the formula you used

just didnt remember

[cyan mesa]

[crisp raptor]

thans I understood this now

.close

[topaz sinew]

Channel closed

Closed by @crisp raptor

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[real blaze]

We need to check the nature of the roots of the cubic equation
X^3-18x-35=0

By descartes rules of sign

[restive inlet]

that isn't a quadratic equation

[real blaze]

Yes typo

@restive inlet

[topaz sinew]

@real blaze Has your question been resolved?

[real blaze]

<@&286206848099549185>

[placid valley]

so what is the equation then? Def not a quadratic though

or is it a typo

are you tryin to solve it or whats your question?

[real blaze]

descartes rule is wrong?

how to find quickly about nature of roots

[topaz sinew]

@real blaze Has your question been resolved?

Channel closed

Closed by @real blaze

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[frail girder]

how do I show that this system of equations has an infinite amount of solutions?

[topaz sinew]

@frail girder Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[neon iron]

How do I determine for which value of the real parameter a>0 the finite and non-zero limit exists

[cursive patrol]

you find the product of the left-most terms of the series expansions of (sinx), ln(1 + x^2), and sqrt(e^4x - 1)

if a exceeds this product, the limit will go to infinity. if it falls short of this product, the limit will go to 0

[neon iron]

use well known limits like sinx/x, ln(1+x)/x, (e^(x)-1)/x

i think

for example ln(1+x²)/x^a
a must be 2 for it to be a nonzero limit

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

@obsidian otter Has your question been resolved?

[obsidian otter]

<@&286206848099549185>

[keen valley]

whats the probability of the final score being 2

[fair thorn]

no

since you have other possibilites

[keen valley]

(0 and 2)

[fair thorn]

*possibilities

e.g. 1 and 1

or 2 and 0

which is separate from 0 and 2

try solving the probabilities for each of these events separately and then adding them together

no

don't do that

what's the probability of 1, 1?

[obsidian otter]

OH nvm I only took probability of 1 only once 🤦‍♂️

[fair thorn]

yea lol

so what's the answer?

[obsidian otter]

1/12

[fair thorn]

absolutely

gj

[obsidian otter]

Thank you!

[fair thorn]

np lol

i didnt even do anything

[obsidian otter]

still thanks for pointing out my mistake haha

.close

[topaz sinew]

Channel closed

Closed by @obsidian otter

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[neon iron]

if f(x) = x^2-2x+1 write an expression representing g(x) if (g(x) = 2f(x+1) -3

[neon iron]

if f(x) = x^2-2x+1 write an expression representing g(x) if (g(x) = 2f(x+1) -3

Im confused how on to do it because of the x+1

[acoustic pecan]

what would you do if i asked for f(5)

[neon iron]

just replace x with 5

[acoustic pecan]

just do the same with x+1

[neon iron]

so I put x+1 instead of x in the f(x) one?

[acoustic pecan]

yup

[neon iron]

alright thank you

[acoustic pecan]

eg if f(x)=5x then f(x+1)=5(x+1)

[neon iron]

thanks

I was confused

cause I tried to do the thing +1

but i didnt work

have a good one

.close

[topaz sinew]

Channel closed

Closed by @frank vector

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lament fractal]

can someone pls help me understand what happened on the 4th step how did we get 3/2 ,3x, and 2x

[robust zenith]

They moved some things around, not much more.

[lament fractal]

what about the 3/2

[robust zenith]

Check out the 3x in the denominator in sin(3x)/(3x). That 3 wasn't there before, so they compensate with the 3 in the numerator of 3/2.

The 2 in the denominator of 3/2 cancels with the 2 in the numerator of (2x)/sin(2x).

[lament fractal]

ohh

thx so much

[robust zenith]

np

[topaz sinew]

@lament fractal Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[placid drum]

for part d why is the 4th term used and not the 5th

btw $f(x)=\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{n+1}}{3^n\cdot n}$

[thorny flame]

Jash

[topaz sinew]

@placid drum Has your question been resolved?

Channel closed

Closed by @placid drum

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[terse crane]

,rotate 270

[terse crane]

i dont get diff quotient

[neon iron]

Do you remember the slope you learn about for lines

you know

y = mx + b

[terse crane]

rise over run

ou

[neon iron]

yeah

so what is m if you remember

[terse crane]

slope

[neon iron]

yes but how u calculate it

[terse crane]

y two minus y one

over x two

minus x one

[neon iron]

yeah

so like

thats exactly what the difference quotient is about

so like

do you know what a secant line is

[terse crane]

yes

goes through two lines

[neon iron]

no

two points

[terse crane]

points

MY BAD

WAIT

I MENT

POINTS

😭😭

[neon iron]

on the graph of a function

so like

[terse crane]

yes

[neon iron]

say

the first point is some point x okay?

[terse crane]

k

[neon iron]

so we have [
m = \f{y_2 - y_1}{x_2-x_1}
] for the slope of a line

[neon iron]

we will try and calculate the slope of the secant line

[terse crane]

kk

[neon iron]

thats what the difference quotient is. It is representing the slope of the secant

anyways x_1 = x like we said

so now x corresponds to f(x) on the graph yes?

[terse crane]

yea

[neon iron]

that's our y_1

so cool

now say the second point x_2 is like a distance h away from x

so x_2 = x+ h

clear?

[terse crane]

wdym by x_2

_

[neon iron]

here

[terse crane]

ouh

okok

gotit

[neon iron]

that x_2 corresponds to f(x_2)

but we just said x_2 = x +h

so f(x+h)

putting all together this all basically means

[
m = \f{y_2 - y_1}{x_2 - x_1} = \f{\m f{x+h} - \m f x}{x+h - x} = \f{\m f{x+h} - \m f x}h
]

[neon iron]

that's what the difference quotient is. It is a representation of the slope of the secant line

[terse crane]

yea

[neon iron]

if you are still confused i could link you a video maybw

[terse crane]

do u have any helpful vids

just in case

[neon iron]

check out khan academy they most definitely have something explaining it

[terse crane]

kk

.close

[topaz sinew]

Channel closed

Closed by @terse crane

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[agile harness]

factor the denominator

what do u notice

yes

and if u plug in 1 u get 0

substitute

like let x=1

u get -1/0

which is undefined

so we have to do more work

there’s a vertical asymptote at x=1

so it’s going to approach either infinity or negative infinity

so we just need to know if the other factors make it negative or positive

coming from the left of 1

vertical asymptotes occur when the denominator =0

so since we’re coming from the left of one it’s really like 0.999

if we take x to be a little less than one

is x-1 positive or negative

is x-2 positive or negative

is x-3 positive or negative

(negative)(negative)(negative)=?

yes

so it should approach negative infinity

yes

the limit =negative infinity

well u can show the algebra

with the factors

and like a sign chart

showing that less than one the factors r all negative

and 3 negatives makes a negative

and a vertical asymptote at zero means itll approach either positive or negative infinity

hold i’ll show u

yea at one

sorry

because it’s in the denominator

setting the denominator =0 gives a vertical asymptote

unless u get 0/0

which dan be different

yes

hold

u make intervals

like less than one they’re all negative

so when u multiply them u get negative

in between 1 and 2 only x-1 is positive

multiplying them u get positive

and so on

and the 1,2, and 3 r just the zeros of the 3 factors

u don’t in this case im just showing u how to determine where a function is positive or negative for all intervals

for rational functions

yup

ur welcome

[topaz sinew]

Channel closed

Closed by @wise bane

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[remote heath]

I started with integration by parts

but it doesnt make any sense to me

since f(x) and g(x) arent given

[gray harbor]

Where’d you get to with integration by parts?

[remote heath]

here

@gray harbor

wait i confused myself

i see now

the answer would only be f(1)g(1) - f(0)g(0)

[gray harbor]

You need a 2

[remote heath]

and ignoring the second part of the formula

yes bc its -2

bc they gave me the value of the second part

i see thanks

.close

[topaz sinew]

Channel closed

Closed by @remote heath

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[west marten]

if i have found my nullity(T) = [-1,1,-1,1]

[west marten]

why does this make the dimnesion = 1

[vernal matrix]

The kernel spanned by (-1, 1, -1, 1)?

[west marten]

yes

[vernal matrix]

Then your basis of the kernel has one element, so dimension is 1

[west marten]

which elements

i see four numbers

[vernal matrix]

The vector (-1, 1, -1, 1)

Do you have the original question?

[west marten]

yh

find A the relative standardbasis for R^4

find ker(T) and im(T)

i dont undertand how it is one dimensional

[vernal matrix]

Because the kernel is spanned by the vector $\pmqty{-1 \ 1 \ -1 \ 1}$

[thorny flame]

@vernal matrix

[west marten]

yes how is that a one dimensional vector

how can a vector be 1 dimesional

that isnt even a line

[vernal matrix]

This is a line

[west marten]

how is that a line

[vernal matrix]

And it's not the vector that is 1 dimensional, but the kernel, because remember that the dimension of a space is how many elements are in a basis

[native moth]

Saying "one dimensional vector" is a bit confusing, I think it means to state 1 dimensional vectorspace

[west marten]

i thought what mattered was linearly independent-ness

[vernal matrix]

It's a scalar multiple of one vector, so a line

[pseudo jetty]

It's the line $\ds \set {\mat[b]{-1\1\-1\1}t \where t \in \R}$

[west marten]

yes i have wrote that on my paper

i must have a completely misunderstood idea of matrices then

[native moth]

Huh

[west marten]

i thought if you have 4 linearly independent things its would span r^4

[vernal matrix]

4 linearly independent vectors

[west marten]

so what exactly does the coeffeicents in front it represent then

[native moth]

Where is 4 linearly independent things here, hmm

[west marten]

what is x1,x2,x3,x4

[vernal matrix]

Those are the entries of your vector

Those are real numbers (considering you're in R^4)

[west marten]

so it isnt (x,y,z,q)

gggggg

so this is a line in a four-dimensional space

so

[-1,1,-1,1]

[pseudo jetty]

$\ds \set {\mat[b]{-t\t\-t\t} \where* t \in \R}$

[west marten]

is a point in R^4

[pseudo jetty]

you could also write it like this

[west marten]

and the span is the set of scalars you can add onto this

[native moth]

Yea it is also one vector

[native moth]

Huh

[west marten]

that would make a line

(-1,1,-1,1) is a point in a four dimensional space and if you times it by a scalar, lets say 2, you get (-2,2,-2,2) and if you keep this up you'll get a line

[native moth]

Ah, "add" part is a bit confusing there

[west marten]

i changed it

[topaz sinew]

@west marten Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[craggy haven]

yeah unfortunately we can't help on quizzes here. good luck!

[topaz sinew]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[winter tartan]

Can someone point out where these steps are wrong? The answer I get is different from the correct answer.
(2x^(ln(x)-2)(2(ln(x))^2-ln(x)+1)

[sweet shard]

what's the question

[winter tartan]

wait

(b)(i) modified, the fact may not be useful

[sweet shard]

what happened here?

both exponential disappeared

[winter tartan]

oh yeah, I used lim[h->0]((e^x-1) / x) = 1

multiplying ((ln(x+2h))-(ln(x))^2)/((ln(x+2h))-(ln(x))^2)

[sweet shard]

that all sounds wrong

[sweet shard]

this is limit as h going to zero, but your function doesn't have h

[winter tartan]

oh wait i meant x -> 0 haha

[sweet shard]

even if you did fix that and apply that to the first line here, that doesn't explain why the second line still has h

once you take the limit of h, there should be no more h variables left

[winter tartan]

as i think (ln(x+2h))-(ln(x))^2 approaches 0 when h approaches 0

wait i have to write it down

i forgot to write lim[h->0] in the next few steps

[sweet shard]

explain the next line

[winter tartan]

use x^2-y^2 = (x+y)(x-y)

[sweet shard]

why is ln(x) multiplying ln(1+ 2h/x) ?

[winter tartan]

uh oh

oh sorry, the ln(x) should not be there

so that makes the answer 2x^ln(x) (ln(x))

but still different

[topaz sinew]

@winter tartan Has your question been resolved?

[sweet shard]

show your answer with the mistake fixed

[winter tartan]

wait

last step should be 2x^(ln(x)-2) ln(x)

[sweet shard]

what did you do from the first to the second lines here

[winter tartan]

use lim[h->0] (ln(1+h)/h) = 1

[sweet shard]

and what did you do here

[winter tartan]

(facepalm)

i will retake my calc for sure

but now i have 2x^(ln(x)-2) only

[topaz sinew]

@winter tartan Has your question been resolved?

[dense rain]

I have no interest in going through this kind of algebra, but the intent of my hint earlier in the day was that it would be helpful if you used the fact that, -under the limit-,

$ln(1+\frac{h}{x}) = h\ln\left[\left(1+\frac{h}{x}\right)^{\frac{1}{h}}\right] = \frac{h}{x}\ln\left[\left(1+h\right)^{\frac{1}{h}}\right]$

so that using the continuity of the natural log, the limit

$\lim_{h\to 0} \ln\left[\left(1+h\right)^{\frac{1}{h}}\right] = \ln(e).$

[thorny flame]

JessicaK

[dense rain]

You were asked to use this fact:

That should be a sign that it should show up somewhere in your work

[topaz sinew]

@winter tartan Has your question been resolved?

[winter tartan]

.close

[topaz sinew]

Channel closed

Closed by @winter tartan

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hardy meteor]

this is the drivation of langrange's equation from hamilton's principle. i don't get from 2.8 to the last equation. first term vanishes but how does second term equal to the following?

[hardy meteor]

from Classical Mechanics by Goldstein page 37

[loud oasis]

the second term is combined with the first integral from (2.7)

since (2.8) only deals with the second integral from (2.7)

[hardy meteor]

oh shit i missed that 😭

im so dumb. thank you

.close

[topaz sinew]

Channel closed

Closed by @hardy meteor

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[balmy spruce]

$f(x)=\begin{cases} (2x+\sqrt{x})^2 ,if \ x\geq 0 \ (2x+\sqrt{-x})^2, if \ x<0
\end{cases}$
\the slope of tangent (T) of f at A(-1,-1) is
\a)1.5
\b)1.65
\c)2.5

[thorny flame]

pirate king

[balmy spruce]

isnt this question wrong or not enough information ?

or am i missing something

A(-1,-1) is not on f

so assuming that this was not chosen by mistake

then A(-1,-1) is on (T)

but thats all

.close

[topaz sinew]

Channel closed

Closed by @balmy spruce

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[olive stream]

can someone give me the formula for teststastistic, if i want to do a hypothesis test about the y intercept of linear regression

[olive stream]

I cannot find it online

[topaz sinew]

@olive stream Has your question been resolved?

[olive stream]

<@&286206848099549185>

[sonic escarp]

https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/12%3A_Correlation_and_Regression/12.02%3A_Simple_Linear_Regression/12.2.01%3A_Hypothesis_Test_for_Linear_Regression

https://www.youtube.com/watch?v=pJ3MzwzL3Ks

[olive stream]

thank you very much

.close

[topaz sinew]

Channel closed

Closed by @olive stream

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[golden sky]

Idk how to do a)

[restive inlet]

apply gradient (slope) formula

[golden sky]

Line ab is perpendicular to line bc

And I calculate gradient first

And since the multiply to - 1

I just solve

Right

Wait

I got the quadratic b^2 - 7b +14 =0

I put it in desmos I got 6 and 1

And since b is greater than 3

It's 6

But

When I use quadratic equation Ion get that

.close

[topaz sinew]

Channel closed

Closed by @golden sky

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ruby obsidian]

Why is the x-coordinate of the center of mass of the upper half of the circle equal to the x coordinate of the center of mass of the full circle?

[ionic oar]

because of symmetry

there is the same amount of mass on either side

which means your x coordinate would always be on the line of the center of the circle

[ruby obsidian]

wait could you explain that in a bit more detail

oh wait

sio like

[ionic oar]

do you intuitively get what a center of mass is

[ruby obsidian]

nono i get ur logic for the circle

i was just thinking about if that same logic owuld work on the caridoid too

ok so to answer "Why is the x-coordinate of the center of mass of the upper half of the circle equal to the x coordinate of the center of mass of the full circle?"

first, the line of the center of the circle is where both sides of the object will have equal amount of mass (assuming the object has constnat desnity)

so even when we're considering just the upper half of an object that is horizontally cut, because that sliced shape will have equal mass on each side from the line of the center of the circle

the x-coord of the center of mass is always on the line of the center of the circle

and this logic applies to any object of constant denisty

would this be a "correct" description?

[topaz sinew]

@ruby obsidian Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hoary wraith]

Good Day!
Quick question, if I have the following function, does that mean that my co-domain is between 0-1?
Or how can I read it?

[vapid sonnet]

Ya co domain [0,1]

Range is different

[hoary wraith]

And because I cant reach all values between 0-1 my function is not surjective?

[meager dawn]

the function is not surjective and it doesn’t satisfy the intermediate value property lol

it doesn’t take any of the values from 1/4 to 3/4

for example

[vapid sonnet]

Oh yes

My mistake

[meager dawn]

if you’re trying to determine whether a function is surjective like this, it’s best to draw the function, draw your codomain on the y-axis (by shading it in maybe) and seeing whether the entire thing you shaded has an x value such that f(x) = y

if all of those steps are possible

if it’s not possible to do that then you have to just reason about the function, which is a bit harder

[meager dawn]

that is right yeah

[hoary wraith]

So when I sketch the function and find gaps like below, I can assume it is not surjective?

[meager dawn]

yes sort of, but like the function can go back down later (if you were given a different, slightly wackier function) if you know that over your entire domain, you’ll never reach that y value then you know that it’s not surjective, in this example i can draw the horizontal line y=1/2 and realize that my function never takes on the value 1/2, which is in our codomain, so we know it’s not surjective

[hoary wraith]

And this part determines my Domain to Co-Domain relation?

So we project from (0-1) to (0-1)?

[meager dawn]

also, if we specify the codomain to be different then maybe it’ll be surjective, for example if the codomain was [0, 1/4) U [3/4, 1] then it would actually be surjective

[meager dawn]

first interval is the domain, second interval is the codomain

[hoary wraith]

Okay great, thanks!

I will have a look at a few examples

.close

[topaz sinew]

Channel closed

Closed by @hoary wraith

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[toxic stirrup]

what does the 15 in L_15 mean

[toxic stirrup]

to split it into 15 parts?

[woeful drift]

probably

[toxic stirrup]

.close

[topaz sinew]

Channel closed

Closed by @toxic stirrup

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fast adder]

Can anyone help me solve two problems about Carnot's cycle?

[ionic oar]

could give it a shot

although the physics server is better for it

[fast adder]

Oh is there one?

[ionic oar]

yeah in #old-network

[fast adder]

Also the problems are in Spanish I'm translating them rq

Thanks I'll join that one

A reversible heat engine works between two thermal reservoirs, one of them at 443K and the other one at 783K. Find the efficiency of the engine. Find the work made by the engine if we provide 7000kcal and the heat transfered to the cold reservoir.

A reversible heat engine operates between two thermal reservoirs, one of them at temperature T and another one at 280K. If it provides 1000kJ/min of heat to the cold reservoir and develops a usable power of 40kW, find the temperature of the hot reservoir.

<@&286206848099549185>

[ionic oar]

do you know how to find the efficiency?

[thorny flame]

Norbert Baudin

[topaz sinew]

@fast adder Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tepid valve]

hi

[tepid valve]

W=true

[icy sky]

thats correct

iirc if you had
(A iff B) iff (B iff C)
then you should have same columns

[tepid valve]

What is iirc/iff

[icy sky]

if i remember correctly

iff is the <=>

[tepid valve]

okey

but its not equal its ^

wait

I misread something

Its not equal it implies

I thought that two parts should be equal, but the one part implies the second one

I understand now

[tepid valve]

you was correct

.close

[topaz sinew]

Channel closed

Closed by @tepid valve

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stray dew]

how do i know whether i can integrate a function or not. say for example

[stray dew]

these two

left picture it should have an integral sign for 4te^2t

the left picture im supposed to do integration by parts

[raven sparrow]

Second picture does not have an anti derivative in terms of elementary functions

[stray dew]

right picture its a new method but how would i confirm that none of the normal integration methods would not work

[stray dew]

wym by elementary functions

[raven sparrow]

It means that you won't be able to integrate it using your normal methods since you can't express its primitive using only powers/trig/logs/exponentials/etc

Now the proof of that is not something of that level

[stray dew]

how can i tell it cant integrate by just looking at it

[raven sparrow]

By looking at it you just learn to recognize those integrals that won't work under any method . Like here, parts won't help whatever you do, and there's just one thing you can u-sub and is gives nothing.

Some others could be sin(sqrt(x))

[stray dew]

ok so by looking at the left picture can i assume i can do integraion by parts because it has two different functions?

what else gives it away

i know i need two parts for it

so i have 2

u and v

[raven sparrow]

Left picture gives it away because the t factor will "simplify" the integral when doing parts

Because the derivative of t is 1

[stray dew]

wouldnt i have 4t as u

du is 4

oh wait

for picking dv, it needs to be something easy to integrate so id go with e^2t

and v would be 1/2e^2t

[raven sparrow]

I'd say, usually, composition of log, sqrt and exponentials are suspicious.

[stray dew]

suspicious as in the equation is less likely to be able to integrate?

or harder

[raven sparrow]

Yeah

[stray dew]

oh ok

ty

[topaz sinew]

@stray dew Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dry hull]

$\sum_{n \geq 2} \frac{x}{n^{1 + x}}$ i need to find for which values of x this converges

[thorny flame]

uwupachkii

[dry hull]

i find x > 1

so that we can compare it to a riemanns serie

[rigid ivy]

x>0 maybe?

[dry hull]

but then the follow up question is the norm of it

oh yeah surely

exercise asks for largest interval

for x = 0 it works

we define $f_n : x \rightarrow \frac{x}{n^{x + 1}}$ and we need to find for $n \geq 2$, $|| f_n|^I_{\infty}$

[thorny flame]

uwupachkii

[dry hull]

i decided i would find the derivative because i dont see obvious marjoration

and the derivative cancels when x = 1

and damn it is correct

so yeah interval is more than >1

[dry hull]

this with x = 0 too

idk why i thought it would diverge if 1+x was not stricly superior than 2

thanks guys !

[topaz sinew]

@dry hull Has your question been resolved?

Channel closed

Closed by @dry hull

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tight rivet]

Is 0.1 correct

[topaz sinew]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[radiant tapir]

first off be careful of your units. 0.1 feet would be a very, very tiny building

it's one mile away

try converting miles to feet first

[tight rivet]

5280

[radiant tapir]

ok good. Now re-do the work with that information 🙂

[tight rivet]

Tan(6)=x/5280 5280tan(6)=x?

555

Is that right

[radiant tapir]

yep seems right to me 🙂

[tight rivet]

@radiant tapir

How do I do this

My vertex is right?

???

@sweet shard

[sweet shard]

plugging in 4 is already wrong

[tight rivet]

How

I thought u plug in x to find y

[sweet shard]

yea but your x is wrong

when the x value is left of the y axis, then that x value is negative

[tight rivet]

4/(2 times 1/2)

For x?

[sweet shard]

no idea how you got this

[tight rivet]

-b/2a

[sweet shard]

a = -1/2

[tight rivet]

Oh

[sweet shard]

even just visually, you should know the x value of the vertex is negative and the y value of the vertex is positive

[tight rivet]

How about find the maximum or minimum value of f in that graph

Does that mean the highest/lowest x intercept

[sweet shard]

no, y = f(x), so min/max of f means min/max of y

[sweet shard]

where in the screenshot are you being asked this

[tight rivet]

I didn’t take the full picture

[topaz sinew]

@tight rivet Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cyan harbor]

Given that Megan is the second place, the formula is technically like this 5p2

[cyan harbor]

Or am I wrong

[wary tulip]

second runner up means 3rd place?

[cyan harbor]

I think that's 2nd place

[wary tulip]

what are champion and first runner-up then?

[cyan harbor]

oh yeah it makes sense

But Megan is already the 2nd runner up

So 5p2 I think

[wary tulip]

if megan is included in the 5 contestants (which i would assume) then it should be 4P2

[cyan harbor]

She is included

Look at 13-14

[wary tulip]

uh that means she's not included in the 5 lol

but also that's information you should have included in the original question

[cyan harbor]

So it's technically 5p3?

[wary tulip]

no

5P2 is right

[cyan harbor]

Oh okay

Thanks

.close

[topaz sinew]

Channel closed

Closed by @cyan harbor

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ancient valve]

What do I do

[woeful drift]

you use the hint

[topaz sinew]

@ancient valve Has your question been resolved?

[ancient valve]

How do I know if it's right based on that tho

[woeful drift]

Because all right triangles satisfy that property, and anything that isn't a right triangle doesn't

[ancient valve]

Where tf do I get 180 from tho in the first one

I do not get it

Nvm I'm stupid

[woeful drift]

They explain in multiple steps where 180 comes from

[ancient valve]

!close

.close

[topaz sinew]

Channel closed

Closed by @ancient valve

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[visual leaf]

The tutorial said that this integral diverges as x^-1/2 is a p function where p=1/2 < 1

What does this even mean?

[visual leaf]

(Like what is a P function and why does this mean it diverges here

[woeful drift]

It refers to expressions of the form 1/x^p

The integral of 1/x diverges, so anything with a smaller power than 1 also diverges

[visual leaf]

I see I see
Why does the integral of 1/x diverge then?

[woeful drift]

Well what is the antiderivative of 1/x?

[visual leaf]

ln|x|+c

Ohhh ok I see

And if u put infinity in for x it goes to infinity so it diverges

[woeful drift]

Indeed

[visual leaf]

Aigh thanks for helping 👍

.close

[topaz sinew]

Channel closed

Closed by @visual leaf

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tight rivet]

How do I do this

[silver wasp]

is this a calculus problem?

[restive birch]

the equation describes a parabola with a maximum turning point

[tight rivet]

No

[tight rivet]

Ok I know that

[silver wasp]

okay do you know how a parabola looks based on the equation?

[tight rivet]

It goes down

[silver wasp]

nice

where is the maximum then?

[tight rivet]

I dunno

-5/2(-0.001)

?

[restive birch]

that is the x-coordinate of the vertex

[tight rivet]

Isn’t that part of the maximum

[restive birch]

yes

to find the vertex from this equation, you have to use the formula u just used

x = -b/2a

to find the axis of symmetry

once u have x, you sub that value into the given equation to find y

then u have vertex (x,y)

[tight rivet]

So is y the maximum profit then?

[restive birch]

yes

[tight rivet]

4400?

[restive birch]

ye

[tight rivet]

Thanks

.close

[topaz sinew]

Channel closed

Closed by @tight rivet

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lime zenith]

We are supposed to use limit comparison with a geometric series to find if the sum of a (n) is convergent or not. I have no clue how to even start this

[worthy storm]

for large n, which term is going to dominate in the numerator? and which term in the denominator?

[topaz sinew]

@lime zenith Has your question been resolved?

[astral thicket]

does B+2=4^n?

[lime zenith]

That part is not intuitive to me, I’d say n^5 would dominate in the numerator but if it wants geometric it should be 4^n? In the denominator it would be 19^3n

I tried making b(n) = 4^n/19^3n but couldn’t figure out from there

Is that the right track?

[worthy storm]

nope, it turns out that 4^n will dominate, it grows much faster than any polynomial (n^5 is a polynomial)

[lime zenith]

😭

[worthy storm]

yes this is what you want to compare with

[lime zenith]

So then the limit would just equal 1 and b(n) would be convergent so the series converges?

[astral thicket]

I don't know what that means

[worthy storm]

why are you typing in this channel

[worthy storm]

yes to both, assuming you can justify both claims and you're not just guessing 😁

[astral thicket]

ok

[lime zenith]

Lmao

Well the limit would equal 1 just because you have terms cancelling out on top and bottom since as n approaches infinity, the other terms can be ignored

And then b(n) is convergent bc it’s a geometric series where abs value or r < 1

So for this one, would you make b(n) equal to (4^.4n/19^(n+3))^6?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lime zenith]

.reopen

[topaz sinew]

✅

[topaz sinew]

@lime zenith Has your question been resolved?

[topaz sinew]

@lime zenith Has your question been resolved?

[lime zenith]

<@&286206848099549185>

😦

[vapid sonnet]

Hey

You need a bn right such that an/bn convergent

[vapid sonnet]

You can use ratio test bro

[lime zenith]

Bruh we didn’t learn that yet

[hearty anvil]

so learn it

[lime zenith]

Im saying that there’s probably a way to solve it without the ratio test that I should know

[hearty anvil]

aight lemme take a gander

[hearty anvil]

is this still the current quesiton

[lime zenith]

The second picture I sent is my current problem, but the instructions are the same

[hearty anvil]

so using limit comparison test you need to determine what you are comparing it to

4n^2 / (19^(n+3)) because its the highest term of both

and u can use that one which happens to be geometric to know if it converges or not

the limit comparison test says that if one converges the other does too

after proving that they are both greater than 0 ofc

[topaz sinew]

@lime zenith Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pulsar sun]

in the above, if I replace n with with 1/j for some real integer j

[pulsar sun]

is that allowed?

[chilly walrus]

no

[pulsar sun]

why btw?

[chilly walrus]

n must be an integer

doing n choose 2k won't make sense then

[pulsar sun]

oh right 🤦‍♂️

well is there like no formula for cos(x/n) then?

[chilly walrus]

btw i am, to an extent, an expert on this because i wrote a 4k word essay on this stuff lol

[chilly walrus]

not a general one

[pulsar sun]

bro i trust u its fine

[pulsar sun]

why is that?

just too tough to generalize?

[chilly walrus]

basically

[pulsar sun]

i do remember bprp finding cos(theta/3) and it being multivalued or smthin like that

[chilly walrus]

what i did is set $T_n(\cos(\frac{\pi}{n})) = \cos{\pi}$

and i get a polynomial

[pulsar sun]

like there were multiple different formulas out of which only 1 was (supposed) to be correct

[chilly walrus]

solving this polynomial would subdivide the angle

[thorny flame]

artemetra

[pulsar sun]

why

[chilly walrus]

is discord media down again

[pulsar sun]

the latex isnt loading

[chilly walrus]

this doesn't load

shit

lol

[pulsar sun]

😐

[chilly walrus]

$d$

[thorny flame]

artemetra

[chilly walrus]

dead

[pulsar sun]

wait u is real right

what if we replace u

[chilly walrus]

you can

you'll get a complex polynomial

[pulsar sun]

💀

[pulsar sun]

why tho? like do we replace with ((e^ix) - e^(-ix))/2?

[chilly walrus]

wait

[chilly walrus]

oh

yeah it's fine

that's how chebyshev polynomials were derived tho

lol

[pulsar sun]

let me see if i can make sense of this

[pulsar sun]

what okay this getting a lil messy

so

we have polynomials

[chilly walrus]

yes

[pulsar sun]

with this formula

[chilly walrus]

yes

[pulsar sun]

we replace x with cos(u) to get cos(nu) correct

[chilly walrus]

mhm

[pulsar sun]

then if replace x with cos(pi/n) why do we get cos(pi) and isnt that -1?

[chilly walrus]

it is -1

$\frac{\pi}{n} \cdot n = \pi$

[thorny flame]

artemetra

[pulsar sun]

Mhm WAIT OH we put pi/n in cos nx i see i see

[chilly walrus]

but also here you need to define what you mean by "formula"

[pulsar sun]

a generalisaiton for all integers n, so something similar to the cos(nx) formula

[chilly walrus]

$\frac{e^{ix/n}-e^{-ix/n}}{2}$

[thorny flame]

artemetra

[chilly walrus]

does that work?

not satisfying tho!

[pulsar sun]

as a substitution? idrk

[pulsar sun]

in place of cos(nx)? no ofc not

[pulsar sun]

ye exactly

[chilly walrus]

in place of cos(x/n)

i made a formula for any integer degree

like $\cos(n\textdegree)$

[pulsar sun]

hmm

[thorny flame]

artemetra

[chilly walrus]

wtf

[pulsar sun]

i suppose i was expecting something like cos(nx) chebyshev polynomial thingy

[chilly walrus]

you understood

[chilly walrus]

that's correct

[pulsar sun]

yes i understood

[chilly walrus]

you can easily multiply the angle inside cos

dividing tho is really hard

[pulsar sun]

Hmm did u try doing x=1/u sub urself ever? if u wrote an essay/paper/whatever on this?

[chilly walrus]

not really since that formula breaks for non-integers

you can try but you are gonna have to do (1/2)! type stuff

[pulsar sun]

gamma func?

[chilly walrus]

yea

[pulsar sun]

oof

hmm..

well tyvm

.close

[topaz sinew]

Channel closed

Closed by @pulsar sun

Use .reopen if this was a mistake.

[chilly walrus]

np

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[arctic rock]

How--?

(10Cr) (1)^10-r x (-x)^r

but that doesnt work