Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

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

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

Step 1.2

The limit at negative infinity of a polynomial of even degree 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.

$\infty$