Question

What is $\underset{x\to 0}{lim}\frac{2(1-\cos x)}{x^2}$ equal to?

• A. $0$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $1$

Answer 1

The correct option is D $1$

$\underset{x\to 0}{lim}\frac{2(1-\cos x)}{x^2}=\underset{x\to 0}{lim}\frac{4{\sin }^2\left(\frac{x}{2}\right)}{x^2}=\underset{x\to 0}{lim}\frac{{\sin }^2\left(\frac{x}{2}\right)}{{\left(\frac{x}{2}\right)}^2}=1$
Option D is true