Question

Evaluate the following limit :

$li{m}_{x\to 0}\frac{1-\cos 2x}{x^2}$

• A. $0$
• B. $1$
• C. $2$
• D. none of these

Answer 1

Answer: (C)

$2$

$li{m}_{x\to 0}\frac{1-\cos 2x}{x^2}$

$=li{m}_{x\to 0}\frac{2{\sin }^{2}x}{x^2}$

$=2li{m}_{x\to 0}(\frac{\sin x}{x}\times \frac{\sin x}{x})$

$=2li{m}_{x\to 0}\frac{\sin x}{x}\times li{m}_{x\to 0}\frac{\sin x}{x}=2\left(1\right)\left(1\right)=2$