Calculus Examples

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

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $\infty$ .

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

Step 1.2

The limit at infinity of a polynomial whose leading coefficient is positive is infinity.

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

Step 2

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

$\infty \cdot \infty$

Step 3

Infinity times infinity is infinity.

$\infty$