Calculus Examples

$lim_{n \to 8} \frac{e^{n}}{2^{n}}$

Step 1

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

$\frac{lim_{n \to 8} e^{n}}{lim_{n \to 8} 2^{n}}$

Step 2

Move the limit into the exponent.

$\frac{e^{lim_{n \to 8} n}}{lim_{n \to 8} 2^{n}}$

Step 3

Move the limit into the exponent.

$\frac{e^{lim_{n \to 8} n}}{2^{lim_{n \to 8} n}}$

Step 4

Evaluate the limits by plugging in $8$ for all occurrences of $n$ .

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Step 4.1

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

$\frac{e^{8}}{2^{lim_{n \to 8} n}}$

Step 4.2

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

$\frac{e^{8}}{2^{8}}$

Step 5

Raise $2$ to the power of $8$ .

$\frac{e^{8}}{256}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{e^{8}}{256}$

Decimal Form:

$11.64436713 \dots$