Calculus Examples

$lim_{x \to 8} 5^{- x}$

Step 1

Move the limit into the exponent.

$5^{lim_{x \to 8} - x}$

Step 2

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

$5^{- lim_{x \to 8} x}$

Step 3

Simplify terms.

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Step 3.1

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

$5^{- 8}$

Step 3.2

Simplify the answer.

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Step 3.2.1

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

$\frac{1}{5^{8}}$

Step 3.2.2

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

$\frac{1}{390625}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{390625}$

Decimal Form:

$2.56 \cdot 10^{- 6}$