Calculus Examples

$\frac{1}{0.001} - \frac{1}{e^{0.001} - 1}$

Step 1

Divide $1$ by $0.001$ .

$1000 - \frac{1}{e^{0.001} - 1}$

Step 2

To write $1000$ as a fraction with a common denominator, multiply by $\frac{e^{0.001} - 1}{e^{0.001} - 1}$ .

$\frac{1000 (e^{0.001} - 1)}{e^{0.001} - 1} - \frac{1}{e^{0.001} - 1}$

Step 3

Combine the numerators over the common denominator.

$\frac{1000 (e^{0.001} - 1) - 1}{e^{0.001} - 1}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{1000 e^{0.001} + 1000 \cdot - 1 - 1}{e^{0.001} - 1}$

Step 4.2

Multiply $1000$ by $- 1$ .

$\frac{1000 e^{0.001} - 1000 - 1}{e^{0.001} - 1}$

Step 4.3

Subtract $1$ from $- 1000$ .

$\frac{1000 e^{0.001} - 1001}{e^{0.001} - 1}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1000 e^{0.001} - 1001}{e^{0.001} - 1}$

Decimal Form:

$0.49991666 \dots$