Calculus Examples

$lim_{x \to - 8} e^{- (\frac{x}{10})}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$e^{lim_{x \to - 8} - (\frac{x}{10})}$

Step 1.2

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

$e^{- lim_{x \to - 8} \frac{x}{10}}$

Step 1.3

Move the term $\frac{1}{10}$ outside of the limit because it is constant with respect to $x$ .

$e^{- \frac{1}{10} lim_{x \to - 8} x}$

Step 2

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

$e^{- \frac{1}{10} \cdot - 8}$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Move the leading negative in $- \frac{1}{10}$ into the numerator.

$e^{\frac{- 1}{10} \cdot - 8}$

Step 3.1.2

Factor $2$ out of $10$ .

$e^{\frac{- 1}{2 (5)} \cdot - 8}$

Step 3.1.3

Factor $2$ out of $- 8$ .

$e^{\frac{- 1}{2 \cdot 5} \cdot (2 \cdot - 4)}$

Step 3.1.4

Cancel the common factor.

$e^{\frac{- 1}{2 \cdot 5} \cdot (2 \cdot - 4)}$

Step 3.1.5

Rewrite the expression.

$e^{\frac{- 1}{5} \cdot - 4}$

Step 3.2

Combine $\frac{- 1}{5}$ and $- 4$ .

$e^{\frac{- - 4}{5}}$

Step 3.3

Multiply $- 1$ by $- 4$ .

$e^{\frac{4}{5}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$e^{\frac{4}{5}}$

Decimal Form:

$2.22554092 \dots$