Question

$\underset{x\to 0}{\lim }\frac{1-\cos 2x}{x}\mathrm{is}$

(a) 0
(b) 1
(c) 2
(d) 4

Answer 1

(a) 0

$$\begin{gathered} \underset{x\to 0}{\lim }\frac{1-\cos 2x}{x} \\ =\underset{x\to 0}{\lim }\frac{2{\sin }^{2}x}{x} \\ =\underset{x\to 0}{\lim }2x\times \frac{{\sin }^{2}x}{x^2} \\ \Rightarrow 0 \end{gathered}$$