Calculus Examples

$lim_{x \to 2} \frac{(2.001) - 2}{{(2.001)}^{2} - 13 \cdot 2.001 + 22}$

Step 1

Evaluate the limit of $\frac{(2.001) - 2}{{(2.001)}^{2} - 13 \cdot 2.001 + 22}$ which is constant as $x$ approaches $2$ .

$\frac{(2.001) - 2}{{(2.001)}^{2} - 13 \cdot 2.001 + 22}$

Step 2

Simplify the answer.

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Step 2.1

Subtract $2$ from $2.001$ .

$\frac{0.001}{{2.001}^{2} - 13 \cdot 2.001 + 22}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Raise $2.001$ to the power of $2$ .

$\frac{0.001}{4.004001 - 13 \cdot 2.001 + 22}$

Step 2.2.2

Multiply $- 13$ by $2.001$ .

$\frac{0.001}{4.004001 - 26.013 + 22}$

Step 2.2.3

Subtract $26.013$ from $4.004001$ .

$\frac{0.001}{- 22.008999 + 22}$

Step 2.2.4

Add $- 22.008999$ and $22$ .

$\frac{0.001}{- 0.008999}$

Step 2.3

Divide $0.001$ by $- 0.008999$ .

$- 0.11112345$