Calculus Examples

$lim_{x \to \infty} x^{x}$

Step 1

Use the properties of logarithms to simplify the limit.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Since the exponent $x \ln (x)$ approaches $\infty$ , the quantity $e^{x \ln (x)}$ approaches $\infty$ .

$\infty$