Calculus Examples

$lim_{x \to 0} x^{\sin (x)}$

Step 1

Use the properties of logarithms to simplify the limit.

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Step 1.1

Rewrite $x^{\sin (x)}$ as $e^{\ln (x^{\sin (x)})}$ .

$lim_{x \to 0} e^{\ln (x^{\sin (x)})}$

Step 1.2

Expand $\ln (x^{\sin (x)})$ by moving $\sin (x)$ outside the logarithm.

$lim_{x \to 0} e^{\sin (x) \ln (x)}$

Step 2

Because there are no values to the left of $0$ in the domain of $e^{\sin (x) \ln (x)}$ , the limit does not exist.

$Does not exist$