Calculus Examples

$lim_{x \to \infty} \frac{\cos (24 x)}{24 x}$

Step 1

Move the term $\frac{1}{24}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{24} lim_{x \to \infty} \frac{\cos (24 x)}{x}$

Step 2

Since $\frac{- 1}{x} \leq \frac{\cos (24 x)}{x} \leq \frac{1}{x}$ and $lim_{x \to \infty} \frac{- 1}{x} = lim_{x \to \infty} \frac{1}{x} = 0$ , apply the squeeze theorem.

$\frac{1}{24} \cdot 0$

Step 3

Multiply $\frac{1}{24}$ by $0$ .

$0$