Calculus Examples

$lim_{n \to 8} {(e)}^{\frac{1}{n}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$e^{lim_{n \to 8} \frac{1}{n}}$

Step 1.2

Split the limit using the Limits Quotient Rule on the limit as $n$ approaches $8$ .

$e^{\frac{lim_{n \to 8} 1}{lim_{n \to 8} n}}$

Step 1.3

Evaluate the limit of $1$ which is constant as $n$ approaches $8$ .

$e^{\frac{1}{lim_{n \to 8} n}}$

Step 2

Evaluate the limit of $n$ by plugging in $8$ for $n$ .

$e^{\frac{1}{8}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$e^{\frac{1}{8}}$

Decimal Form:

$1.13314845 \dots$