Calculus Examples

$\frac{lim_{x \to 0} \sqrt{0.001 + 2} - \sqrt{2}}{0.001}$

Step 1

Evaluate the limit of $\sqrt{0.001 + 2} - \sqrt{2}$ which is constant as $x$ approaches $0$ .

$\frac{\sqrt{0.001 + 2} - \sqrt{2}}{0.001}$

Step 2

Simplify the answer.

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Step 2.1

Add $0.001$ and $2$ .

$\frac{\sqrt{2.001} - \sqrt{2}}{0.001}$

Step 2.2

Evaluate the root.

$\frac{1.41456707 - \sqrt{2}}{0.001}$

Step 2.3

Evaluate the root.

$\frac{1.41456707 - 1 \cdot 1.41421356}{0.001}$

Step 2.4

Multiply $- 1$ by $1.41421356$ .

$\frac{1.41456707 - 1.41421356}{0.001}$

Step 2.5

Subtract $1.41421356$ from $1.41456707$ .

$\frac{0.0003535}{0.001}$

Step 2.6

Divide $0.0003535$ by $0.001$ .

$0.3535092$