Binomial Expansion

[hoary umbra]

I think I can do this

[frail shoal]

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[hoary umbra]

This is my attempt

[untold hamlet]

do yoh know binomail expansion formula

[hoary umbra]

Sort of, but this is the way we have to do it

[untold hamlet]

yeah pascals trisngle is a way for small powers

[hoary umbra]

Is this correct?

[untold hamlet]

yes

Are you in first year of a level maths

[hoary umbra]

Just a unit at my university

Calc101

[untold hamlet]

ah

you know the sigma notation for binomial expansion then right?

[hoary umbra]

I've looked into shortcuts from youtube etc but we need to use this solving for full marks

[hoary umbra]

Do you know how to do this?

[tacit turtle]

i told you how in your other post!

go check it!

[untold hamlet]

I havent done integration of e yet so no sorry

[tacit turtle]

$(x+y)^n=\sum_{k=0}^{n} \binom{n}{k} x^k\cdot y^{n-k}$

[slim veldt]

;( | 追放された興奮

[untold hamlet]

yee that formula

[hoary umbra]

This is my formula sheet

[untold hamlet]

oh so then wouldnt it be

sin(40pi/40) + e^(-80) - sin(0) +1

[tacit turtle]

but use u-subsitution

have you not learned it yet?

[hoary umbra]

I'm learning ahead

[tacit turtle]

i mena the formula sheet works too

[hoary umbra]

Which one applies to this?

[tacit turtle]

try using without formula sheet

u-subsitution

if you want to learn ahead you gotta practice ahead

[hoary umbra]

Should I watch a video or something

[tacit turtle]

it’s very easy and i can teach you

[hoary umbra]

Ok

[tacit turtle]

let’s say we have some function f(g(x))

and we need it’s anti derivative

[hoary umbra]

Yeah

[tacit turtle]

we let u=g(x)

and du=g’(x)dx

let’s say that g’(x) is a constant cause that’s what happens here

(not always the case)

so then we would have $\frac{1}{g’(x)}\int f(u) du$

[slim veldt]

;( | 追放された興奮

[tacit turtle]

(like i said, this is not always the case)

i’m just showing one specific example

so all you have to do now is find g’(x) and antiderivative of f(x)

which is obvious here

[hoary umbra]

yep

[tacit turtle]

so try it

generalized u-sub is more complicated than this

but it still holds the same idea conceptually

of reverse chain rule

[untold hamlet]

chain rule mentioned!!!

[hoary umbra]

So g is e^-2x

[tacit turtle]

f(g(x))=e^-2x

and f(x)=e^x

[tacit turtle]

yes!

[hoary umbra]

What now

[tacit turtle]

solve it now

[hoary umbra]

So I have to do one with the 40 and one with 0 ?

As x

No I have to flip it around?

@tacit turtle

[tacit turtle]

finish solving it

[tacit turtle]

yes

sorry i’m having connection issues

[tacit turtle]

subtract the two and simplify, but yes, that is correct

[tacit turtle]

what is e^0?

[hoary umbra]

Oh right

1

[tacit turtle]

and it’s cos(0), not cos

lol

[tacit turtle]

yeah

sorry for the extremely late response but i had to do a race

[untold hamlet]

Howd it go

[cloud heath]

@hoary umbra

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