Question

Evaluate $\underset{x\to 0}{lim}\frac{(1-\cos x)}{x^2}$.

Answer 1

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

Applying L'Hospital Rule

$⟹\underset{x\to 0}{lim}\frac{0+\sin x}{2x}=\frac{1}{2}\underset{x\to 0}{lim}\frac{\sin x}{x}=\frac{1}{2}$