help-39

[heady sigil]

@half tendon

Specifically my dilemma is this

[
4\pi\int_{-r^{2}}^{-r^{2}}u\sqrt{r^{2}-u^{2}}du+4\pi R\int_{-r}^{r}\sqrt{r^{2}-u^{2}}dx
]

[jolly parrot]

Tim

Tim

[heady sigil]

May have done my math wrong because even desmos is giving me an undefined volume

[heady sigil]

The left term actually just cancels out to zero

[heady sigil]

whoops nevermind just forgot to make it $du$ not $dx$

[jolly parrot]

Tim

[heady sigil]

so there is a legitimate volume I just need to figure how to solve this expression

[
4\pi R\int_{-r}^{r}\sqrt{r^{2}-u^{2}}du
]

[jolly parrot]

Tim

[heady sigil]

Ended up looking for the answer online but this is such a cheap way at bending the rules?? What is the proper way to integrate this expression

[pearl pond]

@heady sigil Has your question been resolved?

[plush bramble]

Which part do you think is "cheating" exactly

[pearl pond]

@heady sigil Has your question been resolved?

[heady sigil]

Where they decide that $\int_{-r}^{r}\sqrt{r^{2}-u^{2}}du$ essentially represents the area of a semi-circle and just convert it into $\frac{1}{2}\pi r^{2}$

[jolly parrot]

Tim

[heady sigil]

I'm unsure how to use u sub to integrate this since I only just finished calc 1 but there has to be a way to properly integrate all the way through to eventually get 4pi^2Rr^2 right?

[pearl pond]

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.

[restive briar]

I dont really know how to prove something seemingly obvious like this. Like i say let $\alpha$ be given. Then $\alpha+\beta=0\implies \beta=-\alpha$. And we know that $-\alpha$ exists its just reflecting the number $\alpha$ across the real and imaginary axis

[jolly parrot]

Luca M

[restive briar]

How can I write a formal proof for something like this though

Like how would I show formally that it is unique also

[summer imp]

You need to prove two things here.
That the inverse exists and that it's unique.

If you take a general complex number x+iy, and you find it's additive inverse?

[restive briar]

-x-iy

[summer imp]

Ok, and you can probably show under the scheme of complex numbers that this indeed constitutes an inverse by just adding them

That's sufficient for existence.

Now assume that you have two of them, so a+b = 0 and a+c = 0.
Can you show that b=c?

[restive briar]

Can i say $a+b=0\implies a=-b$ and $a+c=0\implies a=-c$. Then we can say $-b=-c\implies b=c$ so $\beta$ must be unique

[jolly parrot]

Luca M

[summer imp]

I think that should do the trick,

[pearl pond]

@restive briar Has your question been resolved?

Channel closed

Closed by @restive briar

Use .reopen if this was a mistake.

[pearl pond]

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.

[torn sky]

I just started on trigonometry, and something that I'm curious about is what the functions sin cos and tan actually do, and are useful for. I understand that we can find the opposite length of the triangle by doing:

tan = opposite/adjacent
adjacent * tan = opposite

So my first question that arises when doing this is why will this always work with only using the right side's 40 degree angle? Additionally, my second question is what really the tangent returns? For example if we were to get the tangent of this triangle we would end up with tan(8.39cm/10cm) = 0.839 which essentially just returns a constant. Do we only really use these 3 functions to find other angles/lengths, and not really look at the constants yet?

[pearl pond]

@torn sky Has your question been resolved?

[pearl pond]

@torn sky Has your question been resolved?

[torn sky]

I can rephrase if wished for

[quick star]

yep do that

[torn sky]

So maybe to start off a bit easier, if we wanted to calculate the angles, this is how we would use these functions, correct? That if I wanted to calculate corner C i'd need to use sinus, while in corner B I'd need to use cosinus?

[quick star]

to calculate angle C, you'd need two sides

sine(some angle) = opposite/hypotenuse

there are many such angle that work due to the periodicity of sine

but since we're dealing with an euclidean triangle

we want the non right-angles to sum up to 90

in which case, we can find the only unique angle that works

[torn sky]

Updated

10.2 and 6.1

[quick star]

why can you written sin^(-1) and so on for the other things

[torn sky]

because is that not how we find the angles?

[quick star]

u wouldn't write that out there though

so i would suggest you to remove it altogether for now

[torn sky]

My point more with having those functions there, is if that's how you use them. As in if I wanted corner B i'd need to use cosinus, and not tangent, correct?

[lost whale]

for b cosine,tangent and sine all work

[quick star]

in that case, why would you only assign C with sin^(-1)

u can use any trig functions u like

even csc, cot, and/or sec

[torn sky]

So that kind of more answers my first question, no corner is bound to a single function, you can use whatever function we'd like to use?

[quick star]

if the "ratios" are present then sure?

it's the fact that we now have access

to all three sides of the triangle

so we have the liberty to use any trig functions to compute any of our angles

[quick star]

have u used the unit circle prior? generally that's how one starts to define these elementary trig functions

[torn sky]

not really, this is how the book teaches it

the unit circle comes next chapter

[quick star]

Lol sure i guess

[torn sky]

So if I now were to calculate corner C, I would do

6.1cm/10.2cm = 0.598

With that I'd proceed to do sin^(-1)(0.598) = 36.7 degrees for corner C

[lost whale]

no

[quick star]

this "legend" is wrong

this is from the lense of b

from C the opposite side is AB

not AC anymore

[torn sky]

Does the 90 degree corner have to be on the right side, like so?

[quick star]

meh yeah

the only one that looks like a right angle

is the bottom right angle

u can label it however u like

nobody's stopping u from labeling the top right angle as the 90 degree either

[quick star]

but generally you want your geometric figures to be somewhat representative of the actual situation

[quick star]

yeah so you can imagine that sin(..) is a function that returns the ratio of the opposite/hypotenuse, for now

so sin(A) = 6.1/10.2

[quick star]

u know the output cuz ^

[torn sky]

Yeah so 0.598

But to get the angle we'd need to use sin^-1

[quick star]

do you know inverse functions?

[torn sky]

I believe so, but where I live I'm pretty sure that ^-1 are the inverse functions

[quick star]

so you know that if f and g are inverse then:

f(g(x)) = x and g(f(x)) = x?

[torn sky]

yeah

[quick star]

and u also know that for a function to have an inverse

you need it to be bijective?

[torn sky]

didnt go deep into it, but in short yes

[quick star]

hmmm

[quick star]

for now you can live with this yeah

[torn sky]

Because if I use sin^-1(0.598) I get 36.7 degrees, which is correct according to the book

[quick star]

i mean there are more subtleties to this

but yes for all right triangle problems

this checks out

so yes that's what you'd do

[torn sky]

Alright, so updated again

[quick star]

no need for the "key" in between

it doesn't service much purpose if u have to make one for each angle

[torn sky]

the key?

[quick star]

OAH

the "legend"

[torn sky]

ah

I guess you could easily see it if it's a 90 degree corner triangle, right?

[quick star]

wdym

[torn sky]

since you can easily spot the hypotenuse, you can easily find the adjacent by looking down so then the opposit must be the side that's left

[quick star]

i mean the opposite side is always easy to spot

it's quite literally the opposite side

the hypotenuse is the longest side opposite to the 90 degree

(you would've learnt this in a geometry class)

and yeah

largest angle -> longest side

[torn sky]

So once that's done, what would be the last step to find corner A?

My idea would be to find AB and then use cosinus to find the remaining corner

[quick star]

corner A?

u found angle C

[torn sky]

the angle of corner A

[quick star]

thus you found angle A for free

from geometry, you know that the angles in a triangle sum to 180

[torn sky]

I know that, but if I were to do this using the functions

[quick star]

u can use anything from the lense of A yeah

any trig function

that's bc you have AB too (from pythag; geometry again)

so you can use tan, cos, sin, sec, csc, or cot

but sure if youw ant to use sin, what do you think you should do?

[torn sky]

So my idea here was to use cosinus just for experimental reasons.

What I did was to find AB using b = sqrt(c^2-a^2) = sqrt(10.2^2 - 6.1^2) = 8.175

Then I tried to find the cosinus using 8.175/10.2 = 0.8014

Now the interesting part comes where I dont understand why and what's happening.

If I use sin^-1(0.8014) the correct answer comes out, also 53.3 degrees, but if I were to use cos^-1(0.8014) the wrong answer comes out, also 36.7 degrees

[quick star]

,calc sqrt(10.2^2 - 6.1^2)

[jolly parrot]

Result:

8.1749617736109

[quick star]

,calc acos((sqrt(10.2^2 - 6.1^2))/10.2) * 180/pi

[jolly parrot]

Result:

36.729595509416

[quick star]

why do you say is wrong?

quick sanity check

AB > BC

so angle C > angle A

[torn sky]

53.3 is correct (using sin^-1), but 36.7 is wrong (using cos^-1)

[torn sky]

I'm not sure what you're trying to tell me here 😅

I understand that AB is greater than BC

[quick star]

i'm trying to tell you that your angle C is wrong

if C is 36.7

then A = 90 - 36.7 which is clearly greater than 36.7

so you're admitting that CB > AB

which is false

as you can see

[torn sky]

You're fully correct, the book made a mistake with placing the first letters

Let me quickly calculate it again

[quick star]

dw about the book

just use what you know

[torn sky]

I think I now understand what you meant with that the "legend" is useless

It would work different each time you calculate a different angle, not?

[quick star]

yes

[torn sky]

Yeah okay, that makes perfect sense now

[quick star]

it's opposite and adjacent relative to an angle

it's not fixed

like if u were facing me then your left is my right and vice versa

[torn sky]

As I didnt understand why they also used 6.1/10.2 to find corner C, but once you 'rotate' the triangle you'll see that the values have switched

[quick star]

u can always use the geometry check

larger angle -> larger side

[torn sky]

I think using the legend works a bit better for me now since I'm only just now starting, but I think I'll kind of visualize it instead of writing down as I just now found out it can change depending what angle we're trying to get

Well that took a bit heh, thanks for the help, and your patience ❤️

.close

[pearl pond]

Channel closed

Closed by @torn sky

Use .reopen if this was a mistake.

[quick star]

then u have to make a legend for all 2 angles

[pearl pond]

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.

[wet ember]

I was curious if its okay to approximate my sum as a integral in this way?

because I want to solve for Gn but the Gn is also in the sum, which I do not know how to get it out of the sum

[pearl pond]

@wet ember Has your question been resolved?

[pearl pond]

@wet ember Has your question been resolved?

[pearl pond]

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.

[sand robin]

\textbf{Problem 5.} Decide the validity of the following statements.

1. If $(a_n){n \in \mathbb{N}}$ is a real sequence and $L \in \mathbb{R}$, then $\lim{n \to \infty} a_n = L$ holds if and only if $\lim_{n \to \infty} (a_n - L)^2 = 0$.

2. If $f, h$ are continuous functions on $\mathbb{R}$, and $g$ is defined on $\mathbb{R}$ such that $f(x) \leq g(x) \leq h(x)$ for all $x \in \mathbb{R}$, then $g$ is also continuous on $\mathbb{R}$.

3. If $f, g$ are differentiable functions on $\mathbb{R}$, and $a, L \in \mathbb{R}$, then $\lim_{x \to a} \frac{f'(x)}{g'(x)} = L$ implies $\lim_{x \to a} \frac{f(x)}{g(x)} = L$.

4. If $f$ is a function defined on an open interval $I \subset \mathbb{R}$ and there does not exist a primitive function of $f$ on $I$, then $f$ is not continuous on $I$.

5. If $\sum_{n=1}^\infty |a_n| < \infty$ and $\lim_{n \to \infty} a_n \sqrt{n}$ exists, then $\lim_{n \to \infty} a_n \sqrt{n} = 0$.

[jolly parrot]

Slowaq

[sand robin]

please somebody check my answers

YES
NO
NO
NO
YES

[iron stream]

Why is 5 yes ?

consider a_n in the form k/√n

Then lim n tends infinity a_n√n = 1

[sand robin]

but then this series is not absolutely convergingn is it?

[iron stream]

It's divergent

[sand robin]

yes and it has to converge

[iron stream]

Oh I didn't see !!

[sand robin]

notice the first condition

[iron stream]

Doesn't every continuous fn has a primitive?

[sand robin]

well yes but i suppose there exist functions thats not continous but has primitive function

sign x should have primitive function

[iron stream]

It doesn't ig !

[iron stream]

There was a theorem regarding this !

[sand robin]

,w int sgn x dx

[jolly parrot]

Results provided by WolframAlpha

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

Requested by slowaq

[iron stream]

A discontinuous function is integrable too

The question is about, primitives

[sand robin]

well what if we take 1/x

it has primitive functoin

but isnt continous

[iron stream]

I mean the function and primitive aren't defined at the same point !

[iron stream]

The question reads, "f is defined in an open interval"

[sand robin]

hm alright so then the statement is true?

is there some more rigorous explanation to this rather than the fact that we could not find a function which satisfies these conditions?

[iron stream]

Yeahh

[iron stream]

Nah there was a theorem related to this !

[sand robin]

i only know about one which says that if the function is continous at some open interval then it has primitive function there

but my statement has reversed implication

wait its the same

ffs im done with this bs

i give up on maths

ill go and be a baker or something

[pearl pond]

@sand robin Has your question been resolved?

Channel closed

Closed by @sand robin

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.

[storm agate]

how to solve it with substitution

[storm agate]

I tried to substiute both the cos function and sin and it didnt work

[stable dune]

Separate the integral into each term

[storm agate]

because the stuff with x doesnt cancel out

[stable dune]

Then do a substitution for each new integral

[storm agate]

😦

alright bro

will try that now

[stable dune]

The stuff inside the trig is all linear so its not that bad

[storm agate]

wdym?

@stable dune thank u it worked

,3

❤️

[stable dune]

np

[storm agate]

.close

!close

.close

[rustic gate]

.close

?

bot down ig

[stable dune]

now now, we can discuss rates when you start putting more work in

[urban galleon]

The bots are revolting

A Space Odyssey all over again

[storm agate]

actually was so confused why it didnt work 💀

[warm current]

stop being sentient

[midnight haven]

Hi guys

How to be better in maths 😭🙏

[clever zenith]

play the violin or become a jew

[midnight haven]

I'm cooked

Is there no there options

I tried revising but like it never works

Revision tips 👀

Where the people attt

[spare lark]

||<@&268886789983436800>||

[clever zenith]

I'm a jew

I have the right to say that

[wet swallow]

Lol

[spare lark]

Ok

[wet swallow]

!topic

Bot is down

[spare lark]

Bot is sleepin

[pearl pond]

@storm agate Has your question been resolved?

[storm agate]

.close

[spare lark]

.close

[pearl pond]

Channel closed

Closed by @spare lark

Use .reopen if this was a mistake.

[pearl pond]

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.

[whole wave]

hello!
i am trying to find the adjacent angle of this. sqrt5 is the opposite side and 4 is the hypotenuse.
i'm looking up how to do it and the 2 things i have found are:

• adjacent = sqrt(c^2+a^2)
• adjacent = sqrt(difference of a & c * sum of a & c)

for that first one i can only find ai stuff. for the 2nd one i have found a single video. are either of these legit methods to find the adjacent side?

thanks :D (btw, please ping when responding!)

[gaunt surge]

Are you familiar with the trig functions?

[whole wave]

cos, sine, etc? yes

[plush bramble]

don't use ai to learn math

https://www.syedlearns.co/wp-content/uploads/2021/04/167768488_218533083355223_5467976182138651161_n.png

you have b and c. use algebra to solve for a

[whole wave]

yeah i was super skeptical of the ai, i couldn't find much else which is why i asked here haha

[plush bramble]

trig can also work, but pythagorean theorem is simpler if you know the algebra

feel free to work on it on paper for yourself then check your answer here

[dapper kraken]

arent you supposed to find theta

[plush bramble]

oh both theta and x?

i just thought x

yup my bad i can't read

[plush bramble]

,tex .sohcahtoa

[jolly parrot]

riemann

[plush bramble]

can't get away from trig then

[whole wave]

yeah i'm gonan have an easier time with that when i know the side haha

[plush bramble]

here, do you know what sin(theta) equals?

[whole wave]

this is the question, i have sine but put off the others for now. gonna come back to them later

yep i just have this written out

[plush bramble]

this will give you x

and once you have x you can find cos(theta)

you could also use $\sin^2(\th) + \cos^2(\th) = 1$ to solve for it as well

[jolly parrot]

riemann

[whole wave]

mhm mhm ty :)

.close

[plush bramble]

bot borken i guess

.close

yup

[little olive]

could yall just help me out

its not lettin me open one

and its not lettin yall close this one

[plush bramble]

post your question i guess

[desert burrow]

can someone help me in call?

[dapper kraken]

angle bisector theorem+simmilarity

[pearl pond]

@whole wave Has your question been resolved?

Channel closed

Closed by @whole wave

Use .reopen if this was a mistake.

[pearl pond]

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 temple]

The problem is "the cost of fencing is 50 dollars for each 6-foot section. how much do you save by only installing a fence in the backyard. The full yard is 360 ft, the backyard is 240 ft.

[dapper kraken]

how much fencing would you save?

[hoary temple]

yeah

of i do the backyard

and not full area

[pearl pond]

@hoary temple Has your question been resolved?

[hoary temple]

?

<@&286206848099549185>

brah

[pearl pond]

@hoary temple Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[sturdy horizon]

How do I start this problem?

[stable dune]

you have to do a limit on both sides

[steel canopy]

We need the limit?

[stable dune]

if the limits dont equal each other, then it doesnt exist

[sturdy horizon]

oh

but its a greater than sign

not a greater than or equal to sign

does that not matter?

[stable dune]

doesnt matter

since its a limit

thats the weird thing with limits

[sturdy horizon]

ohh I see

ok damn I was just overthinking it

my prof said nothing about this

[stable dune]

with continuity we treat being arbitrarily close to 0 as being 0

[sturdy horizon]

I see

thank you

[stable dune]

idk if you study math

but if you do then youll learn more of this during analysis

[sturdy horizon]

i just finished pre calc last quarter

so this is like the 2nd week of calc for me

[stable dune]

i see

[sturdy horizon]

ty though :D

.close

[pearl pond]

Channel closed

Closed by @sturdy horizon

Use .reopen if this was a mistake.

[pearl pond]

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.

[inner sparrow]

how can i make a graph "drawing" on desmos using functions? such as polynomial, exponential, sum, difference, product, quotient, logarithmic, and trigonometric functions?

[stable dune]

Do you mean one that draws itself out over time?

[inner sparrow]

noo

just a still

differnet functions in different colors, with domain restrictions, act as lines

and they all create one drawing

like desmos art

[plush moss]

Uh I think you're referring to piece wise expressions

I think

[inner sparrow]

nooo

sorry

its grade 12 advanced functions

we just have to make a picture of a social issue

using these functions

on desmos

[plush moss]

What's the uh

Social issue

[inner sparrow]

im trying to do

[versed mica]

just type the function?

[inner sparrow]

rising sea levels

[inner sparrow]

i really dont know which function to use and how to really make the drawing come together

[plush moss]

You can make a domain restriction with piece wise expressions

[inner sparrow]

i think i said that wrong

not domain restriction

just like

shortening the function

yk

[brave sluice]

y=sinx{0<x<3}

[inner sparrow]

yes

like that

my idea for the drawing was

a sin function to act as the water

[plush moss]

Yea desmos calls those piecewise expressions 😭

[inner sparrow]

and then some sort of parabola to be like a piece of land

and a stick man standing on top of it

and like fire around him

from global warming

[inner sparrow]

ahhh okay thank u

didnt know that

what im struggling with most is transformations to get the lines in the right place

[next panther]

jolly ahh math class 😭🙏

[inner sparrow]

plus we arent allowed to use line functions (like straight lines) or quadratic functions, or absolute values

[inner sparrow]

LMAOAOAOAO

[plush moss]

Uh you can use draggable points

[inner sparrow]

wouldnt that change the function tho

like if i was trying to use a degree 3 polynomial function

would dragging it around change what type of function it is?

[plush moss]

Depends on what variables you associate to the point

That's the math part of this assignment

You can make this point be the turning point of a quadratic

Or just the x and y offset of a function

[inner sparrow]

do i then just substitute the values at that point in the slider section into the equation?

[inner sparrow]

how would i get that function just from a point

[plush moss]

Eg let's look at this example

I use the turning point form of a quadratic

And connect x1 and y1 to be the coordinates of a point

[inner sparrow]

i see

we have to keep it in a certain form though

[plush moss]

Yea sure

Just use the form you want

[inner sparrow]

ok lets say

for this

ignore the a variable

its from the previous equation

how would i drag around this function?

[plush moss]

Uh you can just assign the point to be the x and y transformation

[inner sparrow]

how

[plush moss]

Sub x with x-x_1

[inner sparrow]

can i change that after?

[plush moss]

With some expansion yea

[inner sparrow]

doesnt change the graph

when i move the slider around

how do i do it the way you were describing

[plush moss]

Sub x with x-x_1 not just x_1

[inner sparrow]

ohhhhhhh

shooot okay thank u

Important Notes:

1. Organize Functions into Folders

a- All functions used in your design should be organized into the corresponding folders in Desmos by function type

b- A copy of all the functions used in your summary table must be stored in the “Summary Table” folder in desmos without restrictions.

2. No lines or parabolas in your design.

Linear, quadratic, absolute value functions are not allowed. Functions not covered in this course are not allowed.

You may not use compound or composite functions that simplify to linear or quadratic functions (eg "f" left parenthesis, "x" , right parenthesis equals StartFraction, "x" cubed Over "x" , EndFraction
fx=
x3
x​)

3. Restrictions:

To show part of the graph of a function you must restrict its domain and not its range.

For example: "y" equals 4 "x" cubed plus 5 left brace, 0 less than or equal to "x" less than or equal to 1 , right brace
y=4x3+50≤x≤1 shows the part of the graph with x coordinates between 0 and 1

4. Animation and Shading:

You must animate at least one function in your design using sliders and you must shade at least one part of your design using inequalities.

my teacher mentioned this

she says that we have to restrict the function by its domain not the range

does using the x-x1 change the function form?

like will it still be a polynomial function?

[plush moss]

Well use your math knowledge

Just think about it for a bit

[inner sparrow]

im guessing it becomes a different form

because youre subtracting a value

is that a transformation?

[plush moss]

What is a polynomial function?

[inner sparrow]

a function with powers

[plush moss]

Integer powers

[plush moss]

In this case will our function still be a sum of x terms with integer powers?

[inner sparrow]

yes

i think

would putting f(x) in front of it change the graph?

[plush moss]

Uh no

[plush moss]

Mhm as such it is still a polynomial function

Man I wish I could be in your jolly ahh school

[inner sparrow]

hahahaha

yea this assignment is def out there

how would i go about cutting off the vertical parts of the graph?

cause we arent allowed to restrict the range

[pearl pond]

@inner sparrow Has your question been resolved?

[plush moss]

You should be able to express all range restrictions as domain restrictions

For example if you had this function

And wanted to restrict the range between 2 and 5

Then you'd solve the equations
x^3+2x+5=5 and x^3+2x+5=2

Then those x values would be the values for the domain restriction @inner sparrow

You also have the option of just solving them graphically

Which desmos makes very easy to do by highlighting all intercept and turning points

And allowing you to click on them to see their coordinates

[pearl pond]

@inner sparrow Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[ornate sky]

Hello there, this part I have no idea why and how -3^x/9 becomes 1-(1/9), could anyone help me with that?

[ornate sky]

why instead of minus 3^x/9 its multiplication now?

[sterile turtle]

???

wdym

[ornate sky]

look at the pic

[sterile turtle]

yea

idk what you thinking tho

[ornate sky]

look it was 3^x - (3^x / 9) and below it it was simplified to 3^x(1-(1/9))

[sterile turtle]

yea

whats the problem you see with that

[ornate sky]

i dont understand it at all

[sterile turtle]

ok

[ornate sky]

it was exponentiation and now its just simple multiplication?

[sterile turtle]

this is like saying $2 - 2*･a =2(1-a)$

[jolly parrot]

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

[ornate sky]

may i ask how?

[sterile turtle]

i hate latex anyway you get what it is

[ornate sky]

i might have missed learning this part before moving on

[sterile turtle]

ok lets just replace all the numbers with pronumerala

so we have 3^x = a and 1/9=b

[ornate sky]

alright

[sterile turtle]

we can write 2nd line like $a - ab$ yes?

[jolly parrot]

Sho

[sterile turtle]

highkey i dont need latex for this but

[sterile turtle]

you agree with this right?

[ornate sky]

its about this right?

[sterile turtle]

yep

[ornate sky]

i dont see a in 1/9 =b

ok

i totally missed this part

could u give me a name of this or sth?

[sterile turtle]

nah mate this is just algebra

factorisation?

[ornate sky]

alright i should get back to see what did i missed

ty btw

[sterile turtle]

mk

[ornate sky]

.close

[sterile turtle]

gl

[pearl pond]

Channel closed

Closed by @ornate sky

Use .reopen if this was a mistake.

[pearl pond]

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.

[sly plover]

how do i start

[pearl pond]

@sly plover Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[sturdy finch]

I'm stuck trying to check c

[feral sedge]

What are the hypotheses of the MVT?

[sturdy finch]

f(x) is continuous in [a,b]

differentiable in (a,b)

and f'(c) = (f(b)-f(a))/(b-a)

[feral sedge]

That last one isn't a hypothesis

[sturdy finch]

oh so there is only 2

?

[feral sedge]

I think so yeah

[feral sedge]

This is telling you what happens if the hypotheses are satisfied

[sturdy finch]

oh then it's true

I see

[feral sedge]

Yes

[sturdy finch]

thx for the help

[feral sedge]

np

[pearl pond]

@sturdy finch Has your question been resolved?

Channel closed

Closed by @sturdy finch

Use .reopen if this was a mistake.

[pearl pond]

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.

[torpid cosmos]

Number 2

[torpid cosmos]

I have a question about c)

So it says estimate so im assuming you dont need to actually calculate but im confused on how you actually would calcuate it

This unit is rates of change by the way in advanced functions

I did x = 30

so f(31) - f(29) / 2

34 - 36 /2 = -1

but the answer says that the estimate would be -0.75

[rough forge]

Ideally you would wanna choose x = 20 and x = 40

f(20) is approximately 45 and f(40) = 30

x = 30 lies perfectly within [20,40] and you wanna choose values for which you can use the graph at best

The problem with your choice is you cannot accurately tell what function values you would have x = 29 and x = 31 as opposed to choosing the next best integer values

[torpid cosmos]

i see

but it gives the same answer

LOL

= -1

eh

ill probably ask the teacher

its ok ty

.close

[pearl pond]

Channel closed

Closed by @torpid cosmos

Use .reopen if this was a mistake.

[rough forge]

(f(40)-f(20))/(40-20) = (30-45)/(20) = -15/20 = -3/4

[pearl pond]

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.

[steel flare]

$f(x) - f(x-1) = x^4$ Solve for f(x)

[jolly parrot]

kronium_

[coarse harbor]

Any other restrictions for f?

Continuity, for example?

[steel flare]

its continuous

no

[elfin stirrup]

notice that

$f(x) = f(x-1) + x^4 = f(x-2) + (x-1)^4 + x^4$

[jolly parrot]

tobi

[steel flare]

yes

[cobalt hinge]

||summation relation||?

[coarse harbor]

Because we can just define f on [0, 1) arbitrarily and from there find f on the rest of the real line using f(x) = f(x-1) + x⁴

[steel flare]

telescoping series...

[cobalt hinge]

yes yes

[steel flare]

will it work?

[cobalt hinge]

it will be sufficient

but try the other methods first

[steel flare]

such as

[steel flare]

what does that even mean

can you derive a function from this?

[elfin stirrup]

first try to give a statement for all natural numbers or Integers

using induction

[steel flare]

i have no idea what that means

[cobalt hinge]

like, it will be sufficient to solve for f(x) using telescoping

[steel flare]

great so can YOU DERIVE A FUNCTION FRom this single equation?

[cobalt hinge]

yes.

[steel flare]

teach me

master

this forbidden power

it will make so

so strong

that the world will bend to my will

[coarse harbor]

This will produce a large family of functions satisfying the equation

So I guess an interesting question would be to figure out which of those functions are continuous

[elfin stirrup]

If we want to calculate f(3) we can do that by

$f(3) = f(2) + 3^4 = f(1) + 2^4 + 3^4 = f(0) + 1^4 + 2^4 + 3^4$

[cobalt hinge]

lmfao

[jolly parrot]

tobi

[cobalt hinge]

oh no

i deleted my thing

one sec

[steel flare]

imma be honest i just said yes its continuous idk what the function is

yes

[cobalt hinge]

,texsp ||$\sum_{k=1}^n k^4-\sum_{k=1}^n (k-1)^4=n^4$||

[jolly parrot]

;(

[steel flare]

😦

thats the function?

It should be a polynomial function right

[elfin stirrup]

the things you need

[steel flare]

Is there a way to derive this polynomial function EASILY?

[cobalt hinge]

it is

[elfin stirrup]

to find your function here is to know how it acts in Intervall of length 1

[steel flare]

ok

[elfin stirrup]

why?

[coarse harbor]

Alright, let f be some arbitrary continuous function on [0, 1). We can now find all values on [1, 2) using f(x) = f(x-1) + x⁴. Obviously f turns out to be continuous on [1, 2).
We want f to be continuous in the neighborhood of 1 as well, so we want lim_{x -> 1-} f(x) = f(1) = f(0) + 1⁴

Similarly we can find all values on [-1, 0) and write down a condition for continuity at 0, and so on.

[cobalt hinge]

i have proved this before

its somewhere in my notebook

let me see if i can find it

[steel flare]

proof isn't what i want

its the exact opposite of what I want

I want the polynomial equation

[elfin stirrup]

this is how the function behaves for natural numbers

[steel flare]

yes

now what

[cobalt hinge]

we can prove that its a degree 5 polynomial

[elfin stirrup]

then we also have this

[steel flare]

yes

so

[steel flare]

i really dont care about what we can or cant prove, this isn't one of those questions like "prove the sum of the angles of a triangle is 180 deg" Nah, here we find the function

WAIT

THAT

MAKES

IT

easy?

Look

ik a way

[cobalt hinge]

...

continue

[steel flare]

we know that f(n) is $\sum_{i=1}^n i^4$

[elfin stirrup]

• f(0)

[jolly parrot]

kronium_

[steel flare]

ok forget that

fr

just for now

just assume this

[elfin stirrup]

you can calculate that sum

for general n

[steel flare]

$f(n) = \sum_{i=1}^n i^4$

[jolly parrot]

kronium_

[steel flare]

just assume this now

ASSUME THIS FOR Nowe

we also know

its a 5th degree polynomial

so look

now lets find the function g(n)

[coarse harbor]

or do we

[steel flare]

where g(n) = f(n-1)

[coarse harbor]

Why would it be a polynomial in the first place

[steel flare]

look

[steel flare]

shut up and listen and stop asking me to prove the most basic things in existence

[elfin stirrup]

$\sum_{i=1}^n i^4 = \frac{n(n+1)(2n+1)(3n^2+3n-1)}{30}$

[steel flare]

please

[jolly parrot]

tobi

[steel flare]

so look

[elfin stirrup]

this can be proved by induction

[coarse harbor]

It's not basic though?

[steel flare]

its sad your mind cant comprehend it

look

the sum of the an arithmetic sequence is told by a quadratic sequence

a quadratic sequence is told by cubic

cubic by quartic

and so on

now pay attention

[coarse harbor]

Yes but there're infinitely many functions that pass through points of the form (n, \frac{n(n+1)(2n+1)(3n^2+3n-1)}{30})

[elfin stirrup]

I don't know why he says it has to be a polynomial, I think there are infinely many continues function satisfying this

[elfin stirrup]

ys

[steel flare]

$g(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f$

[jolly parrot]

kronium_

[elfin stirrup]

thats why I said you probably need information in atleast one Intervall

of length 1

[steel flare]

g(0) = 0

so f = 0

we need 5 terms

to prove the sequence

[coarse harbor]

Instead of insulting me you could at least remember that we're looking for an f defined on R, not just N: #help-39 message

[steel flare]

Im trying to explain but you keep interuppting me, Im onto smth im not sure if it works

g(0) = 0 so f = 0

[elfin stirrup]

I mean if you just exchange n with x we are probably already done, for the question statement, and f(0) can be any real number then

[coarse harbor]

Yep, that's what I suggested starting with: #help-39 message

[steel flare]

g(1) = 1

g(2) = 17

correct me if im wrong

g(3) = 98

and so on

this gives us a linear pair of equations

which can be solved using a matrix

also 'a' can be solve for if Ik have a few more terms

[coarse harbor]

Yes, but this only gives one solution. What if there are other continuous functions satisfying that relation?

[steel flare]

It's just frustrating to be asked to prove every little thing when I'm onto something like in school

proving comes later

theory must flourish

[coarse harbor]

I didn't want to interrupt your solution, sorry. I was trying to be instructive and pointed out a potential oversight

[elfin stirrup]

every x in R can be written as x = n + alpha, where alpha is in (0,1) and n is an integer, then use the recursion formula

let x be positive for now then

$f(x) = \sum_{i=1}^n i^4 + f(\alpha)$

[coarse harbor]

yep

[jolly parrot]

tobi

[elfin stirrup]

otherwise for negative x you probably get a minus sign

[coarse harbor]

yes
UPD: no

[elfin stirrup]

I am however not sure how someone would continue from here

[steel flare]

so guys

im satisfied

i got my answer

just lettting u know

[coarse harbor]

This function will be automatically continuous on each interval of the form (k, k+1), so it's enough to ensure continuity at integer points

[elfin stirrup]

ah sure, so we can give a class of functions satisfying this then

[coarse harbor]

For any $n$ we want
$$\lim_{x \rightarrow n-} f(x) = \lim_{x \rightarrow n+} f(x),$$
$$\lim_{x \rightarrow n-} \sum_{j=1}^{n-1}j+f({x}) = \lim_{x \rightarrow n+} \sum_{j=1}^{n}j+f({x})$$

[jolly parrot]

EQUENOS

[elfin stirrup]

so I guess we probably use this here then

$\sum_{i=1}^n i^4 = \frac{n(n+1)(2n+1)(3n^2+3n-1)}{30}$

[jolly parrot]

tobi

[elfin stirrup]

but actually that notation is very weird

because inside the limit n should not be an integer

[coarse harbor]

We now have
$$\sum_{j=1}^{n-1}j^4 + \lim_{\alpha \rightarrow 1-} f(\alpha) = \sum_{j=1}^n j^4 + \lim_{\alpha \rightarrow 0+} f(\alpha)$$

[elfin stirrup]

j^4 but yeah

[coarse harbor]

oops yeah

[jolly parrot]

EQUENOS

[steel flare]

$\frac{2ax^3}{6} + \frac{3bx^2}{6} + \frac{cx}{6}$

[jolly parrot]

kronium_

[steel flare]

wait what

no

$\frac{2x^3 + 3x^2 + x}{6}$

[jolly parrot]

kronium_

[coarse harbor]

oh damn

[elfin stirrup]

$\sum_{i=1}^{n-1} i^4 = \frac{(n-1)((n-1)+1)(2(n-1)+1)(3(n-1)^2+3(n-1)-1)}{30} = -n/30 + n^3/3 - n^4/2 + n^5/5$

[jolly parrot]

tobi

[steel flare]

HHAHAHAHA

I DERIVE IT

IK HOW TO DERIVE

the functions

that tell us

[coarse harbor]

Nice, could you please share your answer here when you finish deriving?

[steel flare]

simple

its really

quite simple

so

[coarse harbor]

ikr

[elfin stirrup]

xDD

[steel flare]

Assume you wish to find the sum of an 'n' degree polynomial

the sum of the terms of an nth degree polynomial can be represented by an n+1 degree polynomial

[elfin stirrup]

if you wouldn't mind just share your function f(x) first

that you found

[steel flare]

im too lazy to derive

i'll tell u how it works though

[coarse harbor]

yeah and then you solve a linear system for coefficients

I was asking about f(x) though

[steel flare]

YEZ

but

heres the fun part

'a' and the constant can be found easily

this reduces the linear equation that you need by 2 terms

for example

if you have a 5th degree polynomial

you have to calculate the inverse of a 5x5 matrix

but you can easily find the final constant term and the value of 'a'

if it is the function f(x) you wish to calculate for

then make a function g(x) which you calculate for first where g(x) = f(x-1)

g(x) will also be a n+1 degree polynomial

[elfin stirrup]

are you trying that? but it must hold for all n right

[steel flare]

the first term of the nth degree polynomial

[elfin stirrup]

and even after that its only for x > 0

[steel flare]

that will be the constant

in the n+1 degree polynomial

also evaluate the first n+1 terms of the n+1 degree polynomial

then find their differences

and their differences

do it n+1 times

and you will reach a constant

[pearl pond]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[steel flare]

divide that constant by (n+1)!

that will give you the value of 'a'

so with this a 5th degree polynomial can be reduced to a 3rd degree polynomial

@elfin stirrup

u therE?

[elfin stirrup]

doesn't this prove that no solution exists?

[steel flare]

look

tobi

listen

[elfin stirrup]

sure teach me

[steel flare]

when I tell you a number

I want you to tell me the sum of the fourth powers upto that number

ok

first number is 0

then 1

then 2

then 3

then 4

thats all

if we can find the values of these 4 I can tell you how it works

[coarse harbor]

Hold on we made a mistake. The proper expression for $f(x)$ would be
$$f(x) = f(\alpha) + \sum_{x-j > 0} (x-j)^4$$

[jolly parrot]

EQUENOS

[steel flare]

solution exists

I will prove it to u

[elfin stirrup]

ah yeah yes my bad

[steel flare]

00 01 017 98

what is 98 + 4^4

tell me

ok so

look

[jolly parrot]

tobi

[coarse harbor]

Now the limit below gives us f(1-) = f(0+) + 1

So the final continuity condition is f(1-) = f(0+) + 1

And then we should also check continuity for negative x

[steel flare]

00 01 17 98 354
01 16 81 256
15 65 175
50 110
60

this is what we get

[pearl pond]

@peak vine asked to be reminded <t:1732124725:R>,

[steel flare]

since the constant is '60' and it is a 5th degree polynomial

a = 60/5!

= 1/2

also e = 0

[peak vine]

it seems like you should use the hint

[steel flare]

that makes it si mple right

.close

[pearl pond]

Channel closed

Closed by @steel flare

Use .reopen if this was a mistake.

[coarse harbor]

Yes, you figured out how to find one solution (good job btw). That is, you found f(x) = -x/30 + x^3/3 - x^4/2 + x^5/5.
However, there're many more continuous solutions

[elfin stirrup]

[
\sum_{j=1}^{n-1} (x-j)^4 + \lim_{\alpha \to 1^-} f(\alpha) = \sum_{j=1}^n (x-j)^4 + \lim_{\alpha \to 0^+} f(\alpha)
]

[jolly parrot]

tobi

[elfin stirrup]

right?

[steel flare]

yeah the problem is that the others are ridiculous

[coarse harbor]

Not quite, unless you meant (n-j) in the summation outside of the limit

Also the summation bounds are different (both sums are up to n but one of them starts from j=2)

[coarse harbor]

But mathematically they're not worse than the one you found :)
They're also continuous functions satisfying the relation

[steel flare]

you've been telling me that mumbo jumbo for quite a while now, why dont u give me an example

[coarse harbor]

Let f(x) = x on [0, 1)
In all other points define f(x) using the relation f(x) = f(x - 1) + x^4

So for example on [1, 2) it will be equal to x - 1 + x^4

[steel flare]

i have no idea what that means

[coarse harbor]

The red segment is what we defined on [0, 1)

[steel flare]

that doesn't seem continuous

[coarse harbor]

It is, in fact, continuous

[steel flare]

😭

[pearl pond]

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.

[torpid cosmos]

ohh oops LOL THANK YOU SO MUCH

[torpid cosmos]

.clos

.close

[pearl pond]

Channel closed

Closed by @torpid cosmos

Use .reopen if this was a mistake.

[pearl pond]

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.

[dense plover]

can someone help me with this

[dense plover]

for the second part

why did they do r3 - 4rz instead of r3 - 2r2?

and why is it wrong

as whenever i try it it wrong

nvm i get it

.close

[pearl pond]

Channel closed

Closed by @dense plover

Use .reopen if this was a mistake.

[pearl pond]

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.

[pastel raven]

how can i find all positive solutions to $5+ 3^y = z^3$?

[jolly parrot]

isomorphic to god

[pastel raven]

oh okay, seems that mod 9 works

.close

[pearl pond]

Channel closed

Closed by @pastel raven

Use .reopen if this was a mistake.

[keen rain]

kind of confused whether you referred to integers or not

otherwise it's just solving for z

[pearl pond]

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.

[lone heart]

Find the difference between the upper and lower estimate of sin(x) on 0<= x <= pi/2 for 100 subdivisions

I know the answer is |sin(pi/2) - sin(0)| * pi/200, but why?

pi/200 is Δx, simple enough. But my understanding is sin(pi/2) * Δx is the upper estimate, but why?
isn't sin(pi/2) * Δx just the last rectangle under the curve (when taking right hand values)?

[lone heart]

am I misunderstanding what the question is asking?

[fluid axle]

to your last question, yes

and sin(0) * dx is the first rectangle when taking left hand values

there's a lot of rectangles in common between the two sums

[lone heart]

ohhhhhh

that makes sense

[fluid axle]

(maybe shifted one dx to the right or left, but same area)

[lone heart]

ok I think I understand

the one difference between the two estimates is if they have the leftmost rectangle, or if they instead have the right most one

so we just subtract those

[fluid axle]

yea

[lone heart]

ok thanks

.close

[pearl pond]

Channel closed

Closed by @lone heart

Use .reopen if this was a mistake.

[pearl pond]

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 wharf]

how would i solve

[hoary wharf]

i got to sin^2x =1

[keen rain]

hmm what could you do now

how'd you solve x² = 1

@hoary wharf

.-.

[pearl pond]

@hoary wharf Has your question been resolved?

[hoary wharf]

ah

.close

[pearl pond]

Channel closed

Closed by @hoary wharf

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.

[hybrid basin]

Hello

[hybrid basin]

For the u-sub part here, is that du = xdy or ∂u = x∂y?

[cobalt hinge]

looks like $\partial$ to me, but could be anything

[jolly parrot]

;(

[cobalt hinge]

considering the context, its probably $\partial$

[jolly parrot]

;(

[hybrid basin]

Thanks!

.close

[pearl pond]

Channel closed

Closed by @hybrid basin

Use .reopen if this was a mistake.

[pearl pond]

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.

[mellow abyss]

A uniform solid sphere of mass "m" and radius "R" Can you help me spot my mistake the mass doens't adds up to "m"

[pearl pond]

@mellow abyss Has your question been resolved?

[pearl pond]

@mellow abyss Has your question been resolved?

[warm willow]

.clear

!clear

[pearl pond]

@mellow abyss Has your question been resolved?

[plush bramble]

.close

[pearl pond]

Channel closed

Closed by @plush bramble

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.

[frank shale]

Needed to solve this equation, from my exp/log unit. I applied log to both sides, but then I realized I wasn't really solving for an exp, since it's already given. Can I solve this using log somehow? I got stuck when I needed to separate R from 100.

In the second picture, I solve this without thinking about using log, but curious if I can approach it with log. If the purpose of log func is to help you find the exponent, which I'm given, I'm assuming it's the wrong tool

[cobalt hinge]

yeah, second approach looks better

[summer imp]

You could always divide by 6 in your working with logarithms, and then exponentiate both sides and solve for R

But this amounts to your second method, just with extra steps

[cobalt hinge]

what you can do is this: $\log(\frac52)=6\log(100+R)-6\log(100)$, since by log properties, $\log(\frac{a}{b})=\log(a)-\log(b)$.

[jolly parrot]

;(

[cobalt hinge]

let this sink in for a moment

[summer imp]

In general, equations that need logarithms will have their variables in the exponent. Here you really have a polynomial equation (if you expanded the parentheses)

[cobalt hinge]

this is easily solvable for R with a bit of manipulation

but again, second solution is better.

[frank shale]

ahh yeah, I was also thinking about converting it like this too since I saw I could apply quotient law, but it's just the variable inside that thew me off, how would you eventually separate and isolate it

[frank shale]

ahh I see

[cobalt hinge]

exponentiating both sides again

see now it’s kinda pointless

but you could still do it ig

regardless it leads to that second solution

[frank shale]

could you please show me, probably is something super basic but my brain isn't seeing it rn

actually I can probably search it up, anyway thanks again

.close

[pearl pond]

Channel closed

Closed by @frank shale

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.

[bronze coyote]

$f(x) = 1 + x + x^2 ...... + x^n\ xf'(x) = x + 2x^2 + 3x^3 + ....... + nx^n\ $let$f_1(x) = xf'(x)$ and consider the following family of functions:
$\f_{2}(x)=xf_{1}'(x)\f_{3}(x)=xf_{2}'(x)\......\ f_{q}(x)=xf_{q-1}'(x)\$ proof by induction that $f_2(x)=\sum_{i=1}^{n}i^2x^i$

[jolly parrot]

pppoopoo

[plush bramble]

Can you show the original question

Looks like you typed something wrong

[bronze coyote]

d.ii

[versed mica]

this says show that

you’re not proving anything using induction for f_2

[versed mica]

you wrote d (i)

[pearl pond]

@bronze coyote Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[bronze coyote]

.reopen

[pearl pond]

✅

[bronze coyote]

for second part d.ii

prove by mathematical induction

[summer imp]

This is part d, is the function f meant to be given?

[versed mica]

did you try finding f_q'

[bronze coyote]

this

[versed mica]

we are given that f_{q+1} = xf_q'

[summer imp]

OH yeah mb

[versed mica]

so you just need to find f_q' then multiply it by x

and you should have $f_{q+1} = \sum_{i=1}^n i^{q+1}x^i$

[jolly parrot]

knief

[bronze coyote]

i have this part

[versed mica]

then you completed the induction step

[bronze coyote]

but i don't know how to prove fq => this

fq+1

[versed mica]

if you got this then you already proved it

its how induction works

the base case was done in the earlier parts

then you just showed P(q) => P(q+1)

q was arbitrary so this works

[bronze coyote]

but isn't this just putting q+1 into q

how does this prove anything

[versed mica]

no

you didnt do what i said

$f_{q+1} \coloneq xf_q'$

we assumed as an induction hypothesis that f_q was what we were trying to prove it was

[bronze coyote]

yes

[versed mica]

then just differentiate what you assumed it to be

multiply by x

[versed mica]

and you get this

[jolly parrot]

knief

[versed mica]

much better

bruh

let me change the index

i typed the forbidden combination of letters with i and q

ill use index k

[bronze coyote]

ok

[versed mica]

$f_q = \sum_{k=1}^n k^q x^k$

[jolly parrot]

knief

[versed mica]

lol thats crazy that i cant do i to the q

anyways differentiate this

if you need to expand the sum first then do so

[bronze coyote]

i think i kinda get it

and then i multiply by x

and thas just f q+1

[versed mica]

yes

[bronze coyote]

thank u so much

idk why i ddin't think of differentiating this

.close

[pearl pond]

Channel closed

Closed by @bronze coyote

Use .reopen if this was a mistake.

[pearl pond]

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.