Calculus Examples

$\frac{lim_{x \to 0} x^{3} \cdot \sin (\frac{1}{x})}{\tan^{2} (x)}$

Step 1

Since $x^{3} \cdot - 1 \leq x^{3} \cdot \sin (\frac{1}{x}) \leq x^{3} \cdot 1$ and $lim_{x \to 0} x^{3} \cdot - 1 = lim_{x \to 0} x^{3} \cdot 1 = 0$ , apply the squeeze theorem.

$\frac{0}{\tan^{2} (x)}$

Step 2

Divide $0$ by $\tan^{2} (x)$ .

$0$