Taylor Polynomials

[ginnyflute453]

Let f(x) be a function that has derivatives of all orders for all real numbers. Assume f(0)=2, f'(0)-3, f''(0)= -1, f'''(0)= 4

a. Write the third- degree Taylor polynomial for f(x) about x=0 and use it to approximate f(-0.1)
b. Write the fourth- degree Taylor polynomial for g(x) where g(x)= f(-x[sup:2xcgg3je]2[/sup:2xcgg3je]), about x=0
c. Write the third- degree Taylor polynomial for h(x), where h(x)= (integral from 0 to x) of f(t)dt about x=0

 

[tkhunny]

Well, do it.

Write out a generic Taylor Polynomial. Surely you will see it.

 

[BigGlenntheHeavy]

\(\displaystyle a. \ Let \ f(x) \ = \ ax^{3}+bx^{2}+cx+d, \ (generic \ polynomial \ of \ degree \ 3), \ the \ rest \ should \ be \ elementary.\)