Chapter 1.15, Problem 11P

Use Maclaurin series to evaluate each of the following. Although you could do them by computer, you can probably do them in your head faster than you can type them into the computer. So use these to practice quick and skillful of series to make simple calculations.

$\underset{x\to 0}{\lim }\frac{{\sin }^{2}2x}{x^2}$