Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$8^{lim_{x \to 8} - \frac{1}{x}}$

Step 1.2

Move the term $- 1$ outside of the limit because it is constant with respect to $x$ .

$8^{- lim_{x \to 8} \frac{1}{x}}$

Step 1.3

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

$8^{- \frac{lim_{x \to 8} 1}{lim_{x \to 8} x}}$

Step 1.4

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

$8^{- \frac{1}{lim_{x \to 8} x}}$

Step 2

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

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

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.77110541 \dots$