Originally Posted by

**Spudwad** I am supposed to find the error bound for $\displaystyle sin(x)$ which we are to approximate with $\displaystyle x$ on the interval of [-1,1]. Because $\displaystyle x$ is the first degree Taylor Polynomial, would the upper bound be the second derivative of $\displaystyle sin(x)$:

$\displaystyle f^{(2)}(x)=-sinx$

and then the maximum value on this interval for sin(x) is at 1, so the error bound would be:

$\displaystyle

\frac{-sin(1)} {(3!)}(1^3)$

Is this right? Thanks for the help.