Calculus Examples

$lim_{x \to e} \ln (x^{3})$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the logarithm.

$\ln (lim_{x \to e} x^{3})$

Step 1.2

Move the exponent $3$ from $x^{3}$ outside the limit using the Limits Power Rule.

$\ln ({(lim_{x \to e} x)}^{3})$

Step 2

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

$\ln (e^{3})$

Step 3

Simplify the answer.

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Step 3.1

Use logarithm rules to move $3$ out of the exponent.

$3 \ln (e)$

Step 3.2

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

$3 \cdot 1$

Step 3.3

Multiply $3$ by $1$ .

$3$