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University maths help

Can anyone help me answer these questions:
Reply 1
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Original post by farhanaktar
...


Begin with 4 (i) then.

Do you know the binomial expansion of (1+x)1(1+x)^{-1} ??
Original post by RDKGames
Begin with 4 (i) then.

Do you know the binomial expansion of (1+x)1(1+x)^{-1} ??

Someone doing university maths will for certain know a simple non-rational binomial expansion. They're doomed if they don't lol.
f(x)=12[f(x)+f(x)]Even+12[f(x)f(x)]Odd f(x) = \underbrace{\dfrac{1}{2}[f(x)+f(-x)]}_{\mathrm{Even}} + \underbrace{\dfrac{1}{2}[f(x)-f(-x)]}_{\mathrm{Odd}}
Original post by NotNotBatman
f(x)=12[f(x)+f(x)]Even+12[f(x)f(x)]Odd f(x) = \underbrace{\dfrac{1}{2}[f(x)+f(-x)]}_{\mathrm{Even}} + \underbrace{\dfrac{1}{2}[f(x)-f(-x)]}_{\mathrm{Odd}}


Quite neat.
Original post by RDKGames
Quite neat.

Thank you.
Reply 7
yeah i know but after doing the binomial expansion what should i do
Original post by farhanaktar
yeah i know but after doing the binomial expansion what should i do


You should get a sum consisting of powers of x. Separate this infinite sum into two infinite sums; one consisting of terms with even powers only, and the other consisting of odd powers only. These two infinite sums are your two functions, one of which is even and another of which is odd.
Reply 9
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ill ask you later about these question but can you walk me through the exercise 5 and 6 please
Original post by farhanaktar
ill ask you later about these question but can you walk me through the exercise 5 and 6 please

5) would be splitting the domain into intervals where you can remove the absolute values from the function in each interval, so, eg

|x| = -x when x<0
x when x>=0


For 4), Id do post 5. Just add to get the even and difference to get the odd.
(edited 4 years ago)

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