Question

$\underset{x\to 0}{lim}\frac{1-\cos x}{x^2}isequalto$

• A. 0
• B. 1/4
• C. 1/2
• D. 1

Answer 1

The correct option is C 1/2

We have,

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

This is $\frac{0}{0}$ form.

So, apply L-Hospital rule,

$\underset{x\to 0}{lim}\frac{0-(-\sin x)}{2x}$

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

$\Rightarrow \frac{1}{2}\underset{x\to 0}{lim}\frac{\sin x}{x}$

Since,

$\underset{x\to 0}{lim}\frac{\sin x}{x}=1$

Therefore,

$\Rightarrow \frac{1}{2}\times 1$

$\Rightarrow \frac{1}{2}$

Hence, this is the answer.