Calculus Examples

$lim_{x \to 9} \ln (e^{x})$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the logarithm.

$\ln (lim_{x \to 9} e^{x})$

Step 1.2

Move the limit into the exponent.

$\ln (e^{lim_{x \to 9} x})$

Step 2

Evaluate the limit of $x$ by plugging in $9$ for $x$ .

$\ln (e^{9})$

Step 3

Simplify the answer.

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Step 3.1

Use logarithm rules to move $9$ out of the exponent.

$9 \ln (e)$

Step 3.2

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

$9 \cdot 1$

Step 3.3

Multiply $9$ by $1$ .

$9$