Calculus Examples

$lim_{x \to 0} \frac{\sqrt{- 0.01 + 2} - \sqrt{2}}{- 0.01}$

Step 1

Evaluate the limit of $\frac{\sqrt{- 0.01 + 2} - \sqrt{2}}{- 0.01}$ which is constant as $x$ approaches $0$ .

$\frac{\sqrt{- 0.01 + 2} - \sqrt{2}}{- 0.01}$

Step 2

Simplify the answer.

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Step 2.1

Add $- 0.01$ and $2$ .

$\frac{\sqrt{1.99} - \sqrt{2}}{- 0.01}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{\sqrt{1.99} - \sqrt{2}}{0.01}$

Step 2.3

Evaluate the root.

$- \frac{1.41067359 - \sqrt{2}}{0.01}$

Step 2.4

Evaluate the root.

$- \frac{1.41067359 - 1 \cdot 1.41421356}{0.01}$

Step 2.5

Multiply $- 1$ by $1.41421356$ .

$- \frac{1.41067359 - 1.41421356}{0.01}$

Step 2.6

Subtract $1.41421356$ from $1.41067359$ .

$- \frac{- 0.00353996}{0.01}$

Step 2.7

Divide $- 0.00353996$ by $0.01$ .

$- - 0.35399644$

Step 2.8

Multiply $- 1$ by $- 0.35399644$ .

$0.35399644$