Calculus Examples

$lim_{x \to 0} \frac{3 (1 - \cos (x))}{x}$

Step 1

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$3 lim_{x \to 0} \frac{1 - \cos (x)}{x}$

Step 2

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.

$3 \cdot 0$

Step 3

Multiply $3$ by $0$ .

$0$