Calculus Examples

$lim_{x \to 2} \ln (x - 1)$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the limit inside the logarithm.

$\ln (lim_{x \to 2} x - 1)$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\ln (lim_{x \to 2} x - lim_{x \to 2} 1)$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $2$ .

$\ln (lim_{x \to 2} x - 1 \cdot 1)$

Step 2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\ln (2 - 1 \cdot 1)$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Multiply $- 1$ by $1$ .

$\ln (2 - 1)$

Step 3.2

Subtract $1$ from $2$ .

$\ln (1)$

Step 3.3

The natural logarithm of $1$ is $0$ .

$0$