第14章§6 - 13

$$\begin{array}{rl}\underset{x\to 0}{lim}\frac{\cos x-1}{x^2}& =\underset{x\to 0}{lim}\frac{1}{x^2}\{(1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots )-1\}\\ & =\underset{x\to 0}{lim}(-\frac{1}{2!}+\frac{x^2}{4!}-\cdots )\\ & =-\frac{1}{2}\end{array}$$