Chapter 1.14, Problem 11P

Show that the Maclaurin series for sin x converges to sin x. Hint: If $f(x)=\sin x,f^{n+1}(x)=\pm \sin x\text{}\text{}or\cos x$, and so $|f^{n+1}(x)|\le 1$ for all x and all n. Let $n\to \infty$ in (14.2).