Calculus Examples

$lim_{x \to 0} \frac{1 - e^{8 (- 0.01)}}{7 (- 0.01)}$

Step 1

Evaluate the limit of $\frac{1 - e^{8 (- 0.01)}}{7 (- 0.01)}$ which is constant as $x$ approaches $0$ .

$\frac{1 - e^{8 (- 0.01)}}{7 (- 0.01)}$

Step 2

Simplify the answer.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $8$ by $- 0.01$ .

$\frac{1 - e^{- 0.08}}{7 (- 0.01)}$

Step 2.1.2

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

$\frac{1 - \frac{1}{e^{0.08}}}{7 (- 0.01)}$

Step 2.1.3

Write $1$ as a fraction with a common denominator.

$\frac{\frac{e^{0.08}}{e^{0.08}} - \frac{1}{e^{0.08}}}{7 (- 0.01)}$

Step 2.1.4

Combine the numerators over the common denominator.

$\frac{\frac{e^{0.08} - 1}{e^{0.08}}}{7 (- 0.01)}$

Step 2.2

Multiply $7$ by $- 0.01$ .

$\frac{\frac{e^{0.08} - 1}{e^{0.08}}}{- 0.07}$

Step 2.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{e^{0.08} - 1}{e^{0.08}} \cdot \frac{1}{- 0.07}$

Step 2.4

Divide $1$ by $- 0.07$ .

$\frac{e^{0.08} - 1}{e^{0.08}} \cdot - 14.\overline{285714}$

Step 2.5

Multiply $\frac{e^{0.08} - 1}{e^{0.08}} \cdot - 14.\overline{285714}$ .

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Step 2.5.1

Combine $\frac{e^{0.08} - 1}{e^{0.08}}$ and $- 14.\overline{285714}$ .

$\frac{(e^{0.08} - 1) \cdot - 14.\overline{285714}}{e^{0.08}}$

Step 2.5.2

Multiply $e^{0.08} - 1$ by $- 14.\overline{285714}$ .

$\frac{- 1.18981525}{e^{0.08}}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{1.18981525}{e^{0.08}}$

Step 2.7

Replace $e$ with an approximation.

$- \frac{1.18981525}{{2.71828182}^{0.08}}$

Step 2.8

Raise $2.71828182$ to the power of $0.08$ .

$- \frac{1.18981525}{1.08328706}$

Step 2.9

Divide $1.18981525$ by $1.08328706$ .

$- 1 \cdot 1.0983379$

Step 2.10

Multiply $- 1$ by $1.0983379$ .

$- 1.0983379$