help-0

[indigo lotus]

I want to find the limit when h approaches 0

I applied a^2 - b^2 for the terms inside paranthesis

[stuck cape]

lh

[indigo lotus]

any other way than that

[indigo lotus]

so can I say that when h approaches 0, the term ln(1+h/x) approaches 0.

so the whole expression will be zero

?

[vague mirage]

Can you use L'hôpitals?

[stuck cape]

you can take out log after simplification

[indigo lotus]

.

[stuck cape]

i think so

[indigo lotus]

that's not possible lol

[stuck cape]

no its

[indigo lotus]

I am just asking that can this be a correct way of doing the question?

[indigo lotus]

how

[stuck cape]

$\lim_{x \rightarrow a} log\left(f(x)\right) = log\left(\lim_{x \rightarrow a} f(x) \right)$

[ocean seal]

ayushch80

[indigo lotus]

yeah thats what I am saying

[indigo lotus]

.

[stuck cape]

i don't understood

[indigo lotus]

According to me, when h approaches 0, the term ln(1 + h/x) will approach zero as h/x will approach to zero so all that will be left is ln(1) which is equal to 0

so the whole expression will turn out to be zero

Am I right or wrong?

[stuck cape]

y

[indigo lotus]

what?

[stuck cape]

h/x -> 0

[alpine sable]

i want to make a word problem with this equation.

but idk howww

[indigo lotus]

#❓how-to-get-help

[alpine sable]

wait i apologize

am sorry

[indigo lotus]

no problem

.close

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[plain sundial]

what information can i use to find the area of the highlighted triangle?

note: 15 the HK length, not HJ's

[plain sundial]

or is the question wrong

[alpine sable]

is JH tangent to the circle?

[plain sundial]

yes

holy

i just figured out how

ima show u this to make sure im correct

this correct?

[alpine sable]

yeah, that works

but its a right angle triangle, so you could have used tan

[plain sundial]

Yeah you're right

thanks doe

[alpine sable]

np

[plain sundial]

god bless

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[dapper veldt]

I need to find Tn I got (n+1)(3n-1) when I thought there are n+1 elements and then I got n(3n-1) with n elements but the answer is 3n(n+2)

[dapper veldt]

ps. I got to the answer by making it an arithmetic series (I think its called that) with n or n+1 elements and with a d of 2 (and a1 being 2n-1)

then using the sum fromula

formula*

[pseudo ice]

Your a_1 shouldn’t have n in it (as it’s a constant)

Maybe consider the difference between “full” arithmetic series

[dapper veldt]

wdym?

[pseudo ice]

The first term of an arithmetic sequence/series is a constant (i.e. it should not depend on n)

[dapper veldt]

I got that but what do you mean by difference between full arithmetic series?

[pseudo ice]

For the second comment I made, I’m hinting towards working out e.g. the sum from 1 to 4n+1, then subtract the sum from 1 to 2n-3

[dapper veldt]

ooh

I'll try that

Im having trouble figuring out how many terms the sum from 1 to 4n+1 has same for 1 to 2n-3

[pseudo ice]

2n-3= 2( (n - 1) -1) + 1

[dapper veldt]

so for 4n+1 it'd be 2n+1?

[pseudo ice]

Saved me writing it

Check if that ends up getting you the answer, may be fried

[dapper veldt]

It's correct! tysm!

.cl\ose

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[lavish kelp]

How can I factor a^2+3b^2+4ab+2ac+6bc-4b+4c-4
Please use "a" as the variable

[naive valley]

try the quadratic formula if all else fails?

a^2 + (4b + 2c)a + (stuff that does not depend on a) = 0

[lavish kelp]

Whoever just deleted their msg,your pfp was nice

[lavish kelp]

Hm ok

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@lavish kelp Has your question been resolved?

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[fathom girder]

Hey guys

[fathom girder]

Why does this havebto be 5x+3x?

[last ether]

Are they tryna factor it out

[fathom girder]

why can't I use, for example, 4x+4x? It's still the same thing... Or, 3x+5x?

[fathom girder]

Yes

[last ether]

Well no that's because the coefficients have to multiply to the constant

5 • 3 = 15

4 • 4 = 16 ≠ 15

If you use the FOIL identity

[fathom girder]

So I look at the number at the end, e.g. the 15? And by that I figure out what the numbers are?

[last ether]

$$(x+a)(x+b) = x^2 + (a+b)x + ab$$

[ocean seal]

Umbraleviathan

[fathom girder]

Thank you

Oh, by the way, do I have to write 5x+3x in that order, or can I write in any order I want?

[last ether]

Doesn't matter

[fathom girder]

Ok, thanks

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[echo socket]

What's your question?

[last ether]

The oscillation thing it making me doubt l)

Maybe it is 3 but as far as I'm concerned

Oscillations get stupid

[jade dagger]

Are these correct? It’s the simple limits problems, I do not have answer keys to check them unfortunately, any help would be appreciated

Thanks in advance

[echo socket]

The limit in l doesn't seem to exist though

The rest is fine

[echo socket]

Everything correct here

[jade dagger]

Is that I as lemon or l as in India?

[echo socket]

Lemon

The very last limit in the 1st exericse that you've sent

[jade dagger]

I see, thankyou, could you please correct me why? As it approaches 5 from the left side, shouldn’t the function value approach 3?

[echo socket]

As you can see on the graph the function keeps infinitely oscilating there

It keeps jumping between 2 and 4

And doesn't arrive at a particular value in the limit

[jade dagger]

Oooooh wow

Okay, thankyou 🙏

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[late sentinel]

how did he get from the second last part to 4-gprime 0 = 12

oh nvm

im just a dumbass

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[hearty citrus]

where $f(x)=\frac{2x+3}{\sqrt{4x-1}}$, how can I find the range of f, if the range of x is $x>\frac{1}{4}$

[ocean seal]

Krispeh

[marsh rapids]

f clearly goes to infinity, it's continuous so you just need to find the minimum

[hearty citrus]

so f'(x)=0?

[marsh rapids]

That's the most reliable way yes

Arguably also the only reliable way

[hearty citrus]

it iss

then I'll find the derivative and that eill be the end of that

[rocky grove]

I think you can solve for x too

[marsh rapids]

Yeah also that. And then find the domain of the inverse function

[rocky grove]

Yep

While keeping in mind that it should obey the domain

Of the original

[hearty citrus]

ok thanks

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[velvet burrow]

Find the sum of the expression :
A. 4
b. π
c. 3
d. 32/11
e. 2root2

[velvet burrow]

thus is my try, already found the pattern -18+22n to the power of 1/2to the power of n but don't know where to go from here

[thorn monolith]

consider the limit (n^1/n) = 1

[velvet burrow]

nvm, i want to retry the Un, the expression pattern is wrong after i recheck it

[thorn monolith]

oh nvm its 2^n here but it should also give 1 (which gives the answer 4)

[rancid hazel]

i have found the formula to the sequence 4,18,... idk if you already found it

[velvet burrow]

4n^2+2n-2 ?

[rancid hazel]

i got something else

[thorn monolith]

is 4 the right answer though

if it is, you just need to show how to evaluate the limit of what you found (if 4 is indeed the answer, then you found the right formula)

[velvet burrow]

tbh im not really good with limit, can you teach how to use it in this context?

[thorn monolith]

well if you take (1/n )th power of any number, it will approach one but im trying to show that this limit approaches 1 still

[velvet burrow]

i understand about the 1/n part, where 0,5+025 etc. would end up near one but not exactly

[thorn monolith]

@velvet burrow are you allowed to use l'hopital's rule?

i found how to show that limit is 1, but i used l'hopital's rule

if yes use the fact that

oops, there is something wrong this means that limit we are trying to find is 0, while its not let me find it

[velvet burrow]

there are no specific rules for what method you use

[thorn monolith]

okay, i have no idea how i didnt see that, but this works i believe

let me know if there are any unclear steps

okay, i saw that i typed non correct equation on the first screenshot, here is the correct one

if you find the limit of this, you can just multiply this expression by 22 and subtract 18 to get the pattern you found

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@velvet burrow Has your question been resolved?

[velvet burrow]

aight, the explanation seems clear enough for me

[velvet burrow]

the first one was incorrect the second one is, 4n^2 +2n - 2

[velvet burrow]

aight, thank you for the explanation and the proof you have given ✅

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[native brook]

How to they get the -wsin part. It’s obvs F=ma but how do they use the trig

I dunno what I did wrong

[zinc dagger]

U r supposed to make a right triangle with the theta angle and the w vector as the hypotenuse. The legs of this right triangle represent the tangential and radial components of vector w.
(I’m looking at the bottom diagram of the first photo)

[zinc dagger]

Are you trying to solve for the radial component of w?

[native brook]

Yeah thanks I was using the wrong triangle. I wasn’t using the one with (w as hypotenuse, r hat as opposite) I used (w as opposite and r hat as hypotenuse)

[native brook]

Do you know Why can’t you use triangle I used to resolve for the w component in r hat?

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[steady basin]

hello

[jolly mural]

Hello

[steady basin]

@naive valley sry to ping u pal but i got a question regarding the question we did earlier, do u remember we found the conditional distribution of this?

if we wanted to find the variance of this function

would we do ((1/2 x 4) + (1/2 x 25)) - the mean of that squared?

anyone else can answer this if they want

[tacit arch]

You keep pinging individual people

[steady basin]

we did this question before, and he explained it, thats why im asking him since he did it with me before

we literally did it like 20 mins ago

thats why i pinged him

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[dim hinge]

can someone help me clarify which one acts as x axis and which one acts as y?

[dim hinge]

<@&286206848099549185>

[tacit arch]

Show the whole context, F, S

[dim hinge]

is S x axis and F y axis?

[tacit arch]

It doesn't look like it matters

[dim hinge]

i see

but wont the line of regression equation be different depending if S is x or y?

[tacit arch]

Yea but that's your teacher's fault for writing a question with two answers

[dim hinge]

i see

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[steady basin]

how do i find the shaded part?

<@&286206848099549185>

[tacit arch]

Write out the sum

[steady basin]

what sum

[tacit arch]

Definition of expectation for discrete random variables

[steady basin]

dont get how youd do it with Z1Z2

i can do it for Z1 or Z2

[tacit arch]

https://stats.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame/MATH_345__-_Probability_(Kuter)/5%3A_Probability_Distributions_for_Combinations_of_Random_Variables/5.1%3A_Joint_Distributions_of_Discrete_Random_Variables

Example 5.1.2

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[buoyant path]

How do I calculate the limit of this function when x approaches 0?

[buoyant path]

n is a natural number that's greater than or equal to 2 btw.

[abstract fractal]

What have you tried

[buoyant path]

I haven't tried anything, I have no idea how to start lol.

[abstract fractal]

Note that lim x->0 [f(x) + g(x)] = lim x->0 f(x) + lim x->0 g(x)

[buoyant path]

Hmm

[thorny root]

I think $lim x → 0+ (f_n(x))= lim x → 0- (f_n(x))$

[buoyant path]

I need to use the first function.

[abstract fractal]

Don't give away answers

[thorny root]

that was just to show that limit is the same from leftside and the rightside

[buoyant path]

I want to understand how you got that answer lol.

[abstract fractal]

What's lim x->0 1?

[buoyant path]

1

[abstract fractal]

What's lim x->0 e^x?

[buoyant path]

1

[abstract fractal]

What's lim x->0 e^2x?

[buoyant path]

1

So it's 1?

Like 1+1+1+1...

[abstract fractal]

Yes. How many 1s are we adding for a given n?

[buoyant path]

Infinite I guess.

So +inf is the answer?

[alpine sable]

no

[abstract fractal]

No

[thorny root]

nope

[buoyant path]

Then?

[abstract fractal]

Are there infinite things being added for f_n?

It ends at e^(n - 1)x

[buoyant path]

Oh yeah

[thorny root]

goes from e^0x to e^(n-1)x

[buoyant path]

I get that, but I still can't figure out how to get the limit since e^x+e^2x+...+e^(n-1)x is basically just 1+1+...+1

[abstract fractal]

How many e^axs are there

[buoyant path]

n-1

[abstract fractal]

So, along with the initial 1, there are n 1s being added

[buoyant path]

yeah

[abstract fractal]

What do you get when you add n 1s

[tacit arch]

(n-1) 1s?

[abstract fractal]

There are n-1 1s from e^x to e^(n - 1)x, but the function also has a 1 at the start

[buoyant path]

What do I get?

[tacit arch]

Oh yea I read what you wrote wrong

[abstract fractal]

What do you get when you add 3 ones

1 + 1 + 1

[buoyant path]

3

so n

Oh makes sense lol

[abstract fractal]

Yes

[buoyant path]

I get it now, thanks!

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[steep ember]

What went wrong

[thorny root]

the numerator

[steep ember]

Oh it’s up 3 for 2 and x right

[fierce prairie]

yes

$(2x)^3 = 2^3 x^3$

[steep ember]

Bruu im so bad at math

Thx

[fierce prairie]

nah it’s okay 👍

wait i f-ed that up

[plain flame]

you kind of misplaced that exponent

[ocean seal]

Kihei

[fierce prairie]

sorry abt that

[steep ember]

Got it thx guys

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[steady basin]

how is 1 - phi(2) equal to 0.006

[steady basin]

here it says phi(2) is 0.977

1-0.977 is 0.023

[plain flame]

what the hell

perhaps they mistyped 2.5

since 8/3 >= 2.5

,calc 8/3

[ocean seal]

Result:

2.6666666666667

[steady basin]

theres an equality sign tho

hmmm

[limpid turret]

Yeah I think they were drunk

[steady basin]

but still

[steady basin]

HOW MANY MISTAKES

@pseudo ice they did it again

smh

[limpid turret]

https://tenor.com/view/homer-drunk-dancing-change-color-the-simpsons-gif-17827968

[pseudo ice]

https://tenor.com/view/controlling-laugh-laughing-oh-god-thats-funny-funny-thats-hilarious-gif-26533352

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[trim hazel]

Is infinity over infinity a horizontal asymptote?

[abstract fractal]

Not necessarily

[trim hazel]

Why not?

[abstract fractal]

Why would it?

A limit of the form ∞/∞ isn't guaranteed to even exist

[trim hazel]

Well thinking more deeply about it, it depends on which one grows faster right?

Which infinity

[abstract fractal]

And even if it does exist, it's only a horizontal asymptote if the limit is x->∞ or x->-∞

[limpid turret]

You're getting into concepts of early calculus and real analysis

∞ is not real number, so you can't consider it in division

You consider limits

How do functions behave as they approach infinity?

[trim hazel]

It depends doesn’t it?

[limpid turret]

Like, look at y=x/(x+1) and y=x/(2x+1)

Go really far along x (like x going to ∞)

And see what you get

[trim hazel]

The second grows faster. It would be more steep wouldn’t it?

[limpid turret]

Essentially, both functions will be ∞/∞ as x->∞

[limpid turret]

Try graphing it if you have the software

[trim hazel]

I noticed some difference but what is particularly that you telling to pay attention?

[keen mason]

Limits

You familiar with them?

[limpid turret]

What does y approach as x goes toward ∞?

[trim hazel]

Sorta, I’m going over them

[trim hazel]

1 and 1/2

[limpid turret]

yeah

That's your ∞/∞ question

[trim hazel]

They have the same power and will approach whatever the numerator is divided by the denominator

[limpid turret]

It's not really a "definite" thing

[trim hazel]

Okey i see

Thank you

.close

[lone heart]

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[sterile spindle]

What should I substitute X with for part (e)?

[limpid spade]

sqrt(x)

[sterile spindle]

u=√x?

[rocky grove]

Let x=u^2

[sterile spindle]

I tried, but I ended up with

How should I integrate this?

[limpid spade]

Long division directly

But there's a trick

[ruby current]

take out the 2 and do +1 -1

[sterile spindle]

Ok

Wait, like this?

[keen mason]

App name ? Looks good

[sterile spindle]

Microsoft maths

[keen mason]

No like take the 2 outside the integral

[sterile spindle]

Ok

[cunning trout]

Ya and then this

[sterile spindle]

And what should I do next?

[keen mason]

Do what the guy said

[limpid spade]

.

[keen mason]

+1 -1

[ruby current]

append +1 -1 to the numerator

[limpid spade]

Then break into two frucktions

Fractions

[sterile spindle]

Sorry, I didn't quite get the meaning of "append +1,-1" like the denominator should be (u^2+1+(1-1))?

[abstract fractal]

The numerator

[limpid spade]

Nominatot

[keen mason]

The top

[sterile spindle]

Ok

[cunning trout]

Ya so like here I did +1 and -1 and so this can help to break the fractions

[limpid spade]

Should be u^2+1-1

[sterile spindle]

Ok, I got it, thanks

.close

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[vapid steppe]

A quartic function in the form f(x) = ax⁴ + bx³ + cx² + dx + e is such that the coefficients of the quadratic and linear terms are 10 and –18, respectively. Additionally, f(0) = 9 and x = 1 is a root of multiplicity of 2. What is the value of (a + b)?

[vapid steppe]

what to do

[limpid spade]

Lots of info given

[limpid turret]

what have you tried

[vapid steppe]

i got that f(x)=ax^4+bx^3+10x^2-18x+9

[alpine sable]

indeed

you also know x = 1 is a root of 2nd multiplicity

[vapid steppe]

so do i divide synthetically

[alpine sable]

yes

[vapid steppe]

oh wait i just plugged in x=1 and got a+b=-1

is this correct

[alpine sable]

yes

[vapid steppe]

ok ty

.close

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[modest needle]

how to i find the area under a parabola

[alpine sable]

integrate

[limpid spade]

Integrate it

[modest needle]

how do i get the integral

thats what im stuck on

[limpid turret]

https://tenor.com/view/calculus-calculus-for-everyone-new-saint-andrews-college-mitch-stokes-dr-mitch-stokes-gif-23036015

[alpine sable]

send your question

[limpid spade]

Send your question

[alpine sable]

that's not a quadratic

[limpid spade]

That's not even

Eah

[limpid turret]

https://tenor.com/view/graph-calculus-integral-changing-gif-11973884

[gray isle]

riemman sums

[limpid spade]

Seems u need to do it numerically

[modest needle]

can someone explain that pls

[gray isle]

consider first drawing a rough sketch

split the interval [0,1] into 8 equal parts

draw rectangles based on that and using right endpoints

[modest needle]

would that be the answer?

[gray isle]

the answer isn't a diagram or a bunch of words , no

the diagram helps you see what's going on and will lead you to the answer

[limpid turret]

@modest needle have you learned about derivatives yet?

[modest needle]

you mean instaneous rate of change

[limpid turret]

yes

dy/dx

f'(x)

[modest needle]

yeah

[limpid turret]

Okay

Derivatives have nothing to do with this problem, I just needed to know where you are in your learning track

[modest needle]

ok

[limpid turret]

You need to learn about riemman sums next

[modest needle]

like this

[limpid turret]

You approximate area under a curve by drawing a bunch of rectangles under the curve

Yes exactly like that

Problem was saying to do n subintervals

[modest needle]

8

[limpid turret]

With n=8

So that's 8 rectangles to draw

[modest needle]

so where do i put the top of the rectangle

[gray isle]

right end

[limpid turret]

or left

Or middle

[gray isle]

the question specifies they want the right end for this

[limpid turret]

correction: problem says right endpoints

[modest needle]

thanks

if i simplify this is that my answer?

@limpid turret

[limpid turret]

lgtm

[modest needle]

i got it

thanks @limpid turret

.close

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[prime lotus]

10+9

[fallen verge]

do you actually need help with something

[prime lotus]

yea an opinoin

[fallen verge]

opinion*

[prime lotus]

yea srry

[royal plank]

so what is the question

[prime lotus]

10+9

[royal plank]

where are you stuck

[prime lotus]

people say its 19 then other people say its 21 i can take it

[royal plank]

if you can take it there is no problem then

remember to use .close to close the channel

[prime lotus]

but i want an answer what one

[prime lotus]

i know

[royal plank]

whats 9+10?

[prime lotus]

idk 19 or 21

[royal plank]

whats more logical

where are you stuck

[prime lotus]

19

[royal plank]

remember to use .close to close the channel

[prime lotus]

.close

[lone heart]

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[lone heart]

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[zinc shale]

i need help to find the point where the curve changes directions, and the 2 origin points of this "-4\left(x^{2}+4.5x\right)-8"

[zinc shale]

$-4\left(x^{2}+4.5x\right)-8$

[ocean seal]

Good Evil

[zinc shale]

thats what it'll look like, but i need to find the 3 points i asked for

[silver iron]

you mean local extrema and roots?

[little hazel]

yeah that’s what i think

[zinc shale]

i think (i learned that stuff in french)

[broken gazelle]

if you simplify this you get -4x^2-18x-8

just solve that and you get the x i think

[zinc shale]

how ?

[silver iron]

you can take the derivative

and set it equal to 0

sorry, find critical numbers

[broken gazelle]

or use the quadratic formula

[zinc shale]

yeah... that wont work, its $y=-4\left(x^{2}+4.5x\right)-8$

[ocean seal]

Good Evil

[zinc shale]

if it was 0= then it would have been easy

just solve for x

[silver iron]

you would have to expand it

[zinc shale]

how

[silver iron]

multiplying it out

[zinc shale]

?

[silver iron]

the terms in the parentheses would be multiplied by -4

[zinc shale]

that would bring me to the form i had at the start which is

[silver iron]

right

[broken gazelle]

by origin you mean when y=0 right?

[zinc shale]

what do i do with that ?

[zinc shale]

yes

[broken gazelle]

so just put y=0

and you find the points

[silver iron]

^

[zinc shale]

ohhhh

[broken gazelle]

-4 and -1/2

[zinc shale]

ok, thx

one minute, i got more stuff to ask, but i need to look at the lessons

wait

ik how to find the 2 Xs of the origin points

but how do i find the point where the curve changes its direction ?

[broken gazelle]

for the changing direction i think its just a vertix

so use the fertix formula

its this

where its says vertex

[zinc shale]

whats D ?

[broken gazelle]

the D is b^2-4ac

i dont know why its not the triangle

i usually call it with that symbol

[silver iron]

you only need -b/2a

[broken gazelle]

he need the point so both x and y

[zinc shale]

i tried it, and it didnt work

[wary stream]

Do the OR part

[zinc shale]

with

--18/-4*2

[broken gazelle]

you couldnt find where it changes direction or the other thing

[silver iron]

wait a minute

[zinc shale]

which is 18/-8

[silver iron]

u had it in vertex form already

[wary stream]

No they didn't

[zinc shale]

?

[silver iron]

nvm

saw it wrong

[wary stream]

Yes that is the x coord of the vertex

Plug that back into the equation to find the y coord

[broken gazelle]

you can use photomath

its on the playstore

[zinc shale]

if i have the 2 Xs then i already know at what X point the curve will change

i need to know the Y

[broken gazelle]

no you dont

[wary stream]

Those two x values you found are the roots to that equation

[silver iron]

plug in -18/8 for x to find it

[wary stream]

That's where it crosses the x axis

Not the turning point

The turning point is where the vertex is

[zinc shale]

i do, its the point in the middle of those 2

but what is the y

[broken gazelle]

its just in this case that it works with half

usually it doesnt work

you use -b/2a

[wary stream]

Plug that back into the equation to find the y coord

[broken gazelle]

to find the x

[zinc shale]

ok

[zinc shale]

thx

[broken gazelle]

and b^2-4ac/4a to find the y

[zinc shale]

its ok, ik what to do now

thank you all

[wary stream]

Or you can plug in the x value to find the y value

[zinc shale]

yeah, thats easier

[broken gazelle]

well ye you can do that too

but the formula can be useful in some cases

[lone heart]

@zinc shale Has your question been resolved?

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[ocean seal]

random

[wanton pebble]

is there any condition on a1 and a2

you can find that complimentary subsequences are convergent

and they both converge to same limit

[pseudo ice]

Can agree that a_n is bounded (though need to show it explicitly)

[wanton pebble]

okie

you can easily show that an is bounded between a1 and a2

[worn fox]

(You may aswell just assume a1<=a2)

[wanton pebble]

see this sequence is bounded

[pseudo ice]

You want the sequences to converge to the same limit

[wanton pebble]

yes you can easily find that

just put n= 2^n

[half rain]

IS y=x a polynomial function???

[wanton pebble]

umm how can i explain

see if you assume that subsequences of odd terms converge to say l2 and subsequences of even terms converge to l1

[lone heart]

Please read #❓how-to-get-help

[wanton pebble]

can i sens a pic of what i did

[lone heart]

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[terse magnet]

V=1/3π^2h i wanna isolate h. do i just divide

[wary stream]

Not your channel

[untold garden]

Sorry

[terse magnet]

ty

[pseudo ice]

Though of course you would multiply by 3 (or divide by 1/3), but that's the idea

[terse magnet]

i just put 1/3π^2 under V

so

V/1/3π^2=h

[pseudo ice]

Also as a guess you wanted $V = \frac{\pi}{3}r^2 h$ right?

[ocean seal]

chartbit

[terse magnet]

uhh

no no

maybe?

1/3 is multiplied by pi

and r

then sqrt

by 2

[pseudo ice]

Either way it's the same idea

[terse magnet]

okay

how did you make that bot

nvm ill figure

[pseudo ice]

Just multiply/divide by whatever is appropriate to isolate what you want

[terse magnet]

okay ty

[pseudo ice]

It's $\LaTeX{}$

[ocean seal]

chartbit

[pseudo ice]

See #latex-help for more info about it

[terse magnet]

tysm

[pseudo ice]

No worries, hope that helped!

[last ether]

$\latex$

[ocean seal]

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

[last ether]

Fuck you latex

$\LaTeX{}$

[ocean seal]

Umbraleviathan

[lone heart]

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[terse magnet]

what is (f*g)(x)

[near coral]

need context for this

[last ether]

Seems like f(x) • g(x)

Are you sure it's not (f o g)(x)?

[terse magnet]

if this is true thats all i need

[near coral]

is the star multiplication

[terse magnet]

yeah

[near coral]

then yes

[terse magnet]

its not an open dot

[near coral]

so it is a tiny black dot

[terse magnet]

yes

[near coral]

then f(x)g(x)

[terse magnet]

this then?

oh okay

ty

[near coral]

yes

[terse magnet]

ill need help with the fog one in a bit

[near coral]

lol

[terse magnet]

im restudying my learning from last semester

[near coral]

good luck

[terse magnet]

miDterMSss

aisdjagjhsh

thanks

.close

[lone heart]

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[terse magnet]

.reopen

[lone heart]

✅

[terse magnet]

if i multiply

6x by 2x^2

is that 12x^3 or ^2

[near coral]

if you multiply x^2 by x what would you expect to get

[terse magnet]

x^2

my brain is shutting

oh ^3

[near coral]

if you got x^2 back x would be the multiplicative identity lol

aka 1

[terse magnet]

huh

wait so

x^3

[near coral]

yes

[terse magnet]

ty

[last ether]

Ayo

[terse magnet]

composition is so tedious

[lone heart]

@terse magnet Has your question been resolved?

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[terse magnet]

whats fog

[lone heart]

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[terse magnet]

whats fog

[alpine sable]

probably you mean $f \circ g$ which denotes function composition

[ocean seal]

|G| = [G : H]⋅|H|

[alpine sable]

$f \circ g (x) \implies f(g(x))$

[terse magnet]

yes how does the composition work

[ocean seal]

|G| = [G : H]⋅|H|

[terse magnet]

oh

bruh

math is a scam

[prime badge]

science is a scam

nothing special bout math

[terse magnet]

wait

the x dont exist

[alpine sable]

it's the same

$x$ is a free variable

[ocean seal]

|G| = [G : H]⋅|H|

[alpine sable]

it can be anything

[terse magnet]

ik but on my thing its the composition fog multiplied by (x-1)

[alpine sable]

can you show a picture?

[terse magnet]

yeah one sec

20

[alpine sable]

,rotate

[alpine sable]

riemann.

this implies $f(g(x-1))$ @terse magnet

[ocean seal]

|G| = [G : H]⋅|H|

[terse magnet]

hm

ty

[alpine sable]

riemann.

[terse magnet]

let me try to solve

i dont know how to solve this

.close

[lone heart]

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[tawny halo]

how to find x,y and z?

[alpine sable]

too many ways

[tawny halo]

teach me😭

[hidden fable]

you can set up a coefficient matrix

[woven plaza]

Let's begin with the least understandable method

[alpine sable]

time to use cramers rule

[woven plaza]

Yes

[hidden fable]

I mean there's a ton of ways to solve it

[tawny halo]

you guys are smart

[tacit arch]

Doesn't mean people can teach you

[woven plaza]

Just use elimination, do u know how to solve 2 equations having 2 variables

[alpine sable]

LU factorisation time 😋

jk dont LU factorise

[woven plaza]

How do I get cool ppl role

[alpine sable]

be rich

[woven plaza]

Pay to win server L

[alpine sable]

yeah do be what it do be

i am losing it tomorrow 😔

[woven plaza]

[lone heart]

@tawny halo Has your question been resolved?

[lone heart]

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[loud briar]

Hey

[loud briar]

Sorry but i might be stupid, i need to diffrentiate this sum :

so here what i did

but how am i suppose to compute this now?

i dont recognize the sum nt^{n-1}

[naive valley]

where did the -t^2 come from

[loud briar]

started from n =2 so went down to n =1

so i removed t^2

[naive valley]

wouldn't it be -t in that case

when you added the n=1 term, that's t, not t^2

[rocky grove]

Wait

What's the full question?

[naive valley]

also, there's no need for the index to start at n=0 after taking the derivative, although it also doesn't hurt since that term is zero

[loud briar]

one ec

[naive valley]

if you want the derivative in closed form, why not start with the closed form of the original sum?

[loud briar]

Let f from ]-1,1[, the function defined by f(t) =

[rocky grove]

It's starts at 2

Okay

[loud briar]

yh

[rocky grove]

Well

[loud briar]

then what i told my self i remove one term, then diffrentiate and the sum starts from 0

[supple cobalt]

i think it's an infinite geo series

[loud briar]

it is

[supple cobalt]

because it is defined from -1 to 1 right?

[loud briar]

but does not start from 0

ye

[naive valley]

why does it need to start from 0

[supple cobalt]

so t^2 + t^3 + ...

[naive valley]

you can differentiate it term by term, regardless of where it starts

[loud briar]

yes

true

[rocky grove]

$\sum_{n=2}^{\infty} t^n = t^2 + t^3 + t^4 +... \
\frac{\dd{}}{\dd{x}} $\sum_{n=2}^{\infty} t^n = $\sum_{n=2}^{\infty} nt^{n-1}$

[ocean seal]

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

[naive valley]

what is the problem asking for exactly?

a series, or a closed form expression?

[loud briar]

i need to compute f(1/2)

[rocky grove]

Hmm

Does it need the derivative?

[loud briar]

i thought so,
it is not explicit, it was an exam question

[naive valley]

f(1/2) or f'(1/2)

[loud briar]

just give the answer to f'(1/2)

my bad

but i think i found a way to do it

[rocky grove]

f^(1/2)?

Oh okay

[supple cobalt]

wow ok

[naive valley]

start with the closed form expression for the original sum

and differentiate that

[loud briar]

$$
\sum_{n=0}^{\infty} x^n = \frac{1}{1-x}-1-t
\frac{d}{dx} \sum_{n=0}^{\infty} x^n = \frac{1}{(1-x)^2}-1$$

i think it should work doing that no?

[naive valley]

sure

i think it should be +1/(1-x)^2, not -1/(1-x)^2

if i remember how to take derivatives haha

[loud briar]

yh did a typo

new to latex

[naive valley]

nw

[ocean seal]

Elie

[lone heart]

@loud briar Has your question been resolved?

[lone heart]

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[wraith sun]

i can assume any value of t1,t2 ?

[last ether]

Uh

I really wouldn't do that per se

Lemme look at it a bit

[wraith sun]

Ok

[last ether]

Well actually ... v1 and v2 are just direction vectors right?

They're not lines

In that case, you need 2 parameters

$${x(t,s), y(t,s), z(t,s)} = \text{point} + t(v_1) + s(v_2), s,t \in \bR$$

[ocean seal]

Umbraleviathan

[last ether]

Hope this makes sense

Although your point is just the origin so

The plane just literally contains the vectors @wraith sun

And then if you wanna find 3 points, legit just let t = 3 random values

Could be 5, 17, -2, -69420

[wraith sun]

Ohhh i see

Thank you so much

.close

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[proper nebula]

Hey for describing transformations of exponential functions I am confused on how this problem has horizontal compression of log 1/2 I can’t seem to figure out how to get there

[proper nebula]

I’ll post a pic here

I get the rest but I just can’t seem to grasp the horizontal compression of log 1/2

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@proper nebula Has your question been resolved?

[proper nebula]

haha never mind it doesn’t say log it says by 1/2 nvm .close

.close

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[rotund junco]

can somebody please explain the difference between a premise and a conclusion and also which part of the statement is which in nature of proofs

[thorny root]

premise are the axioms we assume to be false or to be true where the conclusion would be the logical statement derived from those axioms

our conclusion can be logically consistent but whetever it's true or false beyond the axioms depends on the factfulness of the axioms

[rotund junco]

what is an axiom?

[thorny root]

a statement that is taken as either true or false which helps us to derive conclusions

such as
a • b = b • a

[rotund junco]

can i send an image of a question im working on?

regarding this

[thorny root]

sure

[rotund junco]

im so confused

[half totem]

Hey I need help with arithmetic and geometric progression

[thorny root]

an implication is where we imply the conclusion from the premise

[half totem]

I can't seem to understand them at all

[thorny root]

this channel is already occupied

[half totem]

How can I make my own?

[thorny root]

check #❓how-to-get-help

[rocky grove]

!help

[lone heart]

Please read #❓how-to-get-help

[rotund junco]

when i look at the statement head on, which section is the premise?

[thorny root]

the prior statement to the implication symbol

(=>)

[rotund junco]

ah i see

yeah yeah

thank you very much

[thorny root]

glad to help

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@rotund junco Has your question been resolved?

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[half totem]

I need help with arithmetic and geometric progression

[rocky grove]

Okay what's the problem itself?

[lone heart]

@half totem Has your question been resolved?

[stuck cape]

*claps

[half totem]

I just don't seem to understand them

I need help with how I can know which progression is increasing

And explaining how the formulas work

[stuck cape]

arithmetic progressions -> ADDITION
geometric progressions -> MULTIPLICATION

[half totem]

Ok and how can I know which is increasing decreasing or monotone

[stuck cape]

arithmetic is either increasing or decreasing based on their common difference

[half totem]

Okay and can you explain to me how to answer this question

So I can get the grasp of the stuff

So it's an arithmetic progression and I need to find a5
a1=3 and S17=323

[stuck cape]

geometric progressions
common ratio > 0 => increasing
common ratio = 0 => 0
common ratio < 0 => increasing and decreasing both

[ocean seal]

ayushch80

[half totem]

Ok thank you

[ocean seal]

ayushch80

[stuck cape]

you can close this channel by .close if you want to

[half totem]

.close

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[desert pine]

Can someone explain how to do this q

[stuck cape]

point of intersection

maybe you were taught in 11th class

[desert pine]

What do I do next

See ik this part

[ocean seal]

Willow

[stuck cape]

#❓how-to-get-help

!help

[lone heart]

Please read #❓how-to-get-help

[desert pine]

How do I find the point of intersection

[stuck cape]

i would have applied graphical approach tho

[desert pine]

How to do that

[raven haven]

equate f(x) = g(x) then solve

[stuck cape]

open desmos and write equations in it

[desert pine]

Is there any other way

I need to know how to solve this

Without calculator help

[desert pine]

Which eq should i equate

There are 4

[raven haven]

f(x) is one equation lol

since g(x) is piecewise

you check for x > 0 and x <= 0

or whatever it was

[desert pine]

I don't understand

[raven haven]

ok first we consider the case x > 0

then g(x) is 3x/2

so equate 3x/2 = x|x| - 1

now if x <= 0 then g(x) is

2x

so 2x = x|x| - 1

[desert pine]

Okay

Then I'll get two quadratic eq

What to do then

??

[raven haven]

solve

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@desert pine Has your question been resolved?

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[slow prairie]

it's 6 i guess

so dbe it's half of the entire area

right?

[slow prairie]

.

ok

yeah

but 12

is also

the area of adm

which is half of the entire area

cuz

u got the be

which is half from ac

from bc

sorry

and bd which is half of ab

and de which is half of ac

and the area of adm is 12

ade

miss click

wait

just go with six

so yeah

if u wanna

do it with the abm

triangle

the area is 12

and dn

is middle line

and the area of bdn

what grade are u

?

[lone heart]

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[steep pike]

In this example, in the 3rd matrix he switches R2 with R3 which causes a sign change. I have 2 questions about this

[steep pike]

Does a sign change always happen when you switch any row with another row

And also, lets say i was to switch another row, would this cause another sign change meaning the whole det(a) becomes positive again