Calculus Examples

$lim_{x \to \infty} (9 - 5 x) e^{x}$

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 $\infty$ .

$lim_{x \to \infty} 9 - 5 x \cdot lim_{x \to \infty} e^{x}$

Step 1.2

Reorder $9$ and $- 5 x$ .

$lim_{x \to \infty} - 5 x + 9 \cdot lim_{x \to \infty} e^{x}$

Step 1.3

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

$- \infty$