Calculus Examples

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

Step 1

Cancel the common factor of $x$ .

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Step 1.1

Cancel the common factor.

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

Step 1.2

Rewrite the expression.

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

Step 2

Since the exponent $\frac{1}{x^{2}}$ approaches $\infty$ , the quantity ${\tan (1)}^{\frac{1}{x^{2}}}$ approaches $0$ .

$0$