Calculus Examples

$lim_{n \to 8} n {(\frac{6}{5})}^{n}$

Step 1

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

$lim_{n \to 8} n \cdot lim_{n \to 8} {(\frac{6}{5})}^{n}$

Step 2

Move the limit into the exponent.

$lim_{n \to 8} n \cdot {(\frac{6}{5})}^{lim_{n \to 8} n}$

Step 3

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

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Step 3.1

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

$8 \cdot {(\frac{6}{5})}^{lim_{n \to 8} n}$

Step 3.2

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

$8 \cdot {(\frac{6}{5})}^{8}$

Step 4

Simplify the answer.

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Step 4.1

Apply the product rule to $\frac{6}{5}$ .

$8 \cdot \frac{6^{8}}{5^{8}}$

Step 4.2

Raise $6$ to the power of $8$ .

$8 \cdot \frac{1679616}{5^{8}}$

Step 4.3

Raise $5$ to the power of $8$ .

$8 \cdot \frac{1679616}{390625}$

Step 4.4

Multiply $8 (\frac{1679616}{390625})$ .

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Step 4.4.1

Combine $8$ and $\frac{1679616}{390625}$ .

$\frac{8 \cdot 1679616}{390625}$

Step 4.4.2

Multiply $8$ by $1679616$ .

$\frac{13436928}{390625}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{13436928}{390625}$

Decimal Form:

$34.39853568$