Calculus Examples

$lim_{x \to 2} 3 \ln (x - 1)$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$3 lim_{x \to 2} \ln (x - 1)$

Step 1.2

Move the limit inside the logarithm.

$3 \ln (lim_{x \to 2} x - 1)$

Step 1.3

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

$3 \ln (lim_{x \to 2} x - lim_{x \to 2} 1)$

Step 1.4

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

$3 \ln (lim_{x \to 2} x - 1 \cdot 1)$

Step 2

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

$3 \ln (2 - 1 \cdot 1)$

Step 3

Simplify the answer.

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Step 3.1

Multiply $- 1$ by $1$ .

$3 \ln (2 - 1)$

Step 3.2

Subtract $1$ from $2$ .

$3 \ln (1)$

Step 3.3

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

$3 \cdot 0$

Step 3.4

Multiply $3$ by $0$ .

$0$