Answer:
a) The 4th degree , 5th degree and sixth degree polynomials



b)The nth degree Taylor polynomial for f(x) centered at x = 0, in expanded form.

Step-by-step explanation:
Given the polynomial function f(x) = log(1+x) …...(1) centered at x=0
f(x) = log(1+x) ……(1)
using formula 
Differentiating Equation(1) with respective to 'x' we get

….(2)
At x= 0

using formula 
Again Differentiating Equation(2) with respective to 'x' we get

….(3)
At x=0

Again Differentiating Equation(3) with respective to 'x' we get

….(4)
At x=0


Again Differentiating Equation(4) with respective to 'x' we get

....(5)


Again Differentiating Equation(5) with respective to 'x' we get

.....(6)
At x=0

Again Differentiating Equation(6) with respective to 'x' we get


and so on...
The nth term is

Step :-2
Taylors theorem expansion of f(x) is

At x=a =0

Substitute all values , we get

On simplification we get
