Calculus Examples

$lim_{x \to 0} \frac{1 - \cos (x)}{x}$

Since $0 \leq \frac{1 - \cos (x)}{x} \leq \frac{x}{2}$ and $lim_{x \to 0} 0 = lim_{x \to 0} \frac{x}{2} = 0$ , apply the squeeze theorem.

$0$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$