Calculus Examples

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

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the exponent $n$ from ${(\frac{1}{x})}^{n}$ outside the limit using the Limits Power Rule.

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

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

${(\frac{1}{8})}^{n}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Apply the product rule to $\frac{1}{8}$ .

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

Step 3.2

One to any power is one.

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