Question

$\lim_{x\to 0} \frac{1-\cos mx}{1-\cos nx}$ is equal to

• A. $\frac{m}{n}$
• B. $\frac{m^2}{n^2}$
• C. $0$
• D. $\frac{n^2}{m^2}$

Hint:

$1-\cos \theta \sim \frac{\theta^2}{2}$ for small $\theta$.

Answer 1

The Correct Option is B

Step 1: $\lim_{x\to 0} \frac{1-\cos mx}{1-\cos nx} = \lim_{x\to 0} \frac{\frac{m^2x^2}{2}}{\frac{n^2x^2}{2}} = \frac{m^2}{n^2}$.}