Question

Let tk(x) be the degree k taylor polynomial of the function f(x)=sin(x) at a=0. suppose you approximate f(x) by tk(x). if |x|≤1, how many terms are needed (that is, what is k) to obtain an error less than 16

Answer 1

Taylor expansion of sin(x) = x - x^3/3!
So we need 3 terms