Question

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

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $2$
• D. none of these

Answer 1

The correct option is A $\frac{1}{2}$

Now,

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

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

$=\frac{1}{2}\times {\left(\underset{\frac{x}{2}\to 0}{lim}\frac{\sin \frac{x}{2}}{\frac{x}{2}}\right)}^2$

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

$=\frac{1}{2}$.