Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

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

Step 1.2

Move the limit inside the logarithm.

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

Step 2

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

$e^{\ln (e)}$

Step 3

Exponentiation and log are inverse functions.

$e$

Step 4

The result can be shown in multiple forms.

Exact Form:

$e$

Decimal Form:

$2.71828182 \dots$