Calculus Examples

$\frac{lim_{x \to e} \ln (x - 1)}{x - e}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the logarithm.

$\frac{\ln (lim_{x \to e} x - 1)}{x - e}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $e$ .

$\frac{\ln (lim_{x \to e} x - lim_{x \to e} 1)}{x - e}$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $e$ .

$\frac{\ln (lim_{x \to e} x - 1 \cdot 1)}{x - e}$

Step 2

Evaluate the limit of $x$ by plugging in $e$ for $x$ .

$\frac{\ln (e - 1 \cdot 1)}{x - e}$

Step 3

Multiply $- 1$ by $1$ .

$\frac{\ln (e - 1)}{x - e}$