Calculus Examples

$lim_{x \to \infty} \sqrt{x} e^{\frac{- x}{2}}$

Step 1

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

$lim_{x \to \infty} \sqrt{x} \cdot lim_{x \to \infty} e^{\frac{- x}{2}}$

Step 2

As $x$ approaches $\infty$ for radicals, the value goes to $\infty$ .

$\infty \cdot lim_{x \to \infty} e^{\frac{- x}{2}}$

Step 3

Since the exponent $\frac{- x}{2}$ approaches $\infty$ , the quantity $e^{\frac{- x}{2}}$ approaches $\infty$ .

$\infty \cdot \infty$

Step 4

Infinity times infinity is infinity.

$\infty$