Chapter 9, Problem 51RE

Limits by power series Use Taylor series to evaluate the following limits.

51. $\begin{array}{l}\underset{x\to 0}{\lim }\frac{\sec x-\cos x-x^2}{x^4}(Hint:\text{The}\text{Maclaurin}\text{series}\text{for}\text{sec}x\text{is}\\ 1+\frac{x^2}{2}+\frac{5x^4}{24}+\frac{61x^6}{720}+\cdots .)\end{array}$