Calculus Examples

$f (- 0.01) = \frac{5 e^{x} - 5 - 5 x}{x^{2}}$

Step 1

Replace the variable $x$ with $- 0.01$ in the expression.

$f (- 0.01) = \frac{5 e^{- 0.01} - 5 - 5 \cdot - 0.01}{{(- 0.01)}^{2}}$

Step 2

Simplify the result.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

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

$f (- 0.01) = \frac{5 (\frac{1}{e^{0.01}}) - 5 - 5 \cdot - 0.01}{{(- 0.01)}^{2}}$

Step 2.1.2

Combine $5$ and $\frac{1}{e^{0.01}}$ .

$f (- 0.01) = \frac{\frac{5}{e^{0.01}} - 5 - 5 \cdot - 0.01}{{(- 0.01)}^{2}}$

Step 2.1.3

Multiply $- 5$ by $- 0.01$ .

$f (- 0.01) = \frac{\frac{5}{e^{0.01}} - 5 + 0.05}{{(- 0.01)}^{2}}$

Step 2.1.4

Add $\frac{5}{e^{0.01}}$ and $0.05$ .

$f (- 0.01) = \frac{5.00024916 - 5}{{(- 0.01)}^{2}}$

Step 2.1.5

Subtract $5$ from $5.00024916$ .

$f (- 0.01) = \frac{0.00024916}{{(- 0.01)}^{2}}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Raise $- 0.01$ to the power of $2$ .

$f (- 0.01) = \frac{0.00024916}{0.0001}$

Step 2.2.2

Divide $0.00024916$ by $0.0001$ .

$f (- 0.01) = 2.49168745$

Step 2.3

The final answer is $2.49168745$ .

$2.49168745$

Step 3