Calculus Examples

$lim_{x \to 8} - \frac{e^{- 5} x}{10}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

$- lim_{x \to 8} \frac{e^{- 5} x}{10}$

Step 1.2

Move the term $\frac{e^{- 5}}{10}$ outside of the limit because it is constant with respect to $x$ .

$- \frac{e^{- 5}}{10} lim_{x \to 8} x$

Step 2

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

$- \frac{e^{- 5}}{10} \cdot 8$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

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

$- \frac{\frac{1}{e^{5}}}{10} \cdot 8$

Step 3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1

Move the leading negative in $- \frac{\frac{1}{e^{5}}}{10}$ into the numerator.

$\frac{- \frac{1}{e^{5}}}{10} \cdot 8$

Step 3.2.2

Factor $2$ out of $10$ .

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

Step 3.2.3

Factor $2$ out of $8$ .

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

Step 3.2.4

Cancel the common factor.

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

Step 3.2.5

Rewrite the expression.

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

Step 3.3

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

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

Step 3.4

Multiply $4$ by $- 1$ .

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

Step 3.5

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

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

Step 3.6

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.7

Combine.

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

Step 3.8

Multiply $- 4$ by $1$ .

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

Step 3.9

Move $5$ to the left of $e^{5}$ .

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

Step 3.10

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.00539035 \dots$