Calculus Examples

$lim_{x \to \infty} \frac{e^{2 x} - e^{3 x}}{e^{3 x} - e^{2 x}}$

Step 1

Cancel the common factor of $e^{2 x} - e^{3 x}$ and $e^{3 x} - e^{2 x}$ .

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Step 1.1

Factor $- 1$ out of $e^{2 x}$ .

$lim_{x \to \infty} \frac{- 1 (- e^{2 x}) - e^{3 x}}{e^{3 x} - e^{2 x}}$

Step 1.2

Factor $- 1$ out of $- e^{3 x}$ .

$lim_{x \to \infty} \frac{- 1 (- e^{2 x}) - (e^{3 x})}{e^{3 x} - e^{2 x}}$

Step 1.3

Factor $- 1$ out of $- 1 (- e^{2 x}) - (e^{3 x})$ .

$lim_{x \to \infty} \frac{- 1 (- e^{2 x} + e^{3 x})}{e^{3 x} - e^{2 x}}$

Step 1.4

Reorder terms.

$lim_{x \to \infty} \frac{- 1 (e^{3 x} - e^{2 x})}{e^{3 x} - e^{2 x}}$

Step 1.5

Cancel the common factor.

$lim_{x \to \infty} \frac{- 1 (e^{3 x} - e^{2 x})}{e^{3 x} - e^{2 x}}$

Step 1.6

Divide $- 1$ by $1$ .

$lim_{x \to \infty} - 1$

Step 2

Evaluate the limit of $- 1$ which is constant as $x$ approaches $\infty$ .

$- 1$