For the equation f(x)=arcsin x, find the taylor polynomial of degree 3 at c=1/2; determine the accuracy of the polynomial at x=(2^1/2)/2. THese are two example problems I am given to learn how to perform these functions. As I have little to no recollection of Calculus from 15 years ago, could anyone help explain them fully so I can work on other questions of this type.

Question

For the equation f(x)=arcsin x, find the taylor polynomial of degree 3 at c=1/2; determine the accuracy of the polynomial at x=(2^1/2)/2.  THese are two example problems I am given to learn how to perform these functions.  As I have little to no recollection of Calculus from 15 years ago, could anyone help explain them fully so I can work on other questions of this type.

anonymous · Answer

Well, start with differentiating 3 steps.
Find f'(x), f''(x) and f'''(x)

anonymous · Answer

Once you have those, just plug into Taylor's theorem and simplify if possible. There's your taylor polynomial.

anonymous · Answer

To determine the accuracy you need to use this formula: http://en.wikipedia.org/wiki/Taylor%27s_theorem#Explicit_formulae_for_the_remainder

anonymous · Answer

$$\xi $$
is any number in between c and x=(2^1/2)/2

anonymous · Answer

I hope this helps! Shoot a question at me if it's needed. The differentiation is the hard part here really.

anonymous · Answer

I show that f'(x)= 1/(1-x^2)^1/2, but how do I get f"(x) and f'"(x)?  Again it has been extremely long since I have done any of this.