Calculus Examples

$lim_{n \to 8} n x^{n + 2}$

Step 1

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

$lim_{n \to 8} n \cdot lim_{n \to 8} x^{n + 2}$

Step 2

Move the limit into the exponent.

$lim_{n \to 8} n \cdot x^{lim_{n \to 8} n + 2}$

Step 3

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

$lim_{n \to 8} n \cdot x^{lim_{n \to 8} n + lim_{n \to 8} 2}$

Step 4

Evaluate the limit of $2$ which is constant as $n$ approaches $8$ .

$lim_{n \to 8} n \cdot x^{lim_{n \to 8} n + 2}$

Step 5

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

Tap for more steps...

Step 5.1

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

$8 \cdot x^{lim_{n \to 8} n + 2}$

Step 5.2

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

$8 \cdot x^{8 + 2}$

Step 6

Add $8$ and $2$ .

$8 x^{10}$