Originally Posted by

**BoombaWoomba** ...Step-by-step explanations if you will. I'd really appreciate it. Anyways, here are some of the problems:

"Find the Taylor polynomial of order four for the function at x=0, and use it to approximate the value of the function at x=0.2."

1. ) 5 sin ( - x )

...

You know the general form of the Taylor polynomial:

......... is the (n-1)th derivative of f.

With your question a = 0.

Calculate the derivatives: Code:

f(x) = 5sin(-x) --> f(0) = 0
f'(x) = -5cos(x) --> f'(0) = -5
f''(x) = 5sin(x) --> f''(0) = 0
f'''(x) = 5cos(x) --> f'''(0) = 5
f''''(x) = -5sin(x) --> f''''(0) = 0

Now plug in all values:

Calculate

Check this result by calculating