Calculus Examples

$lim_{x \to - 5} \frac{8 (- 5.0001) + 40}{{(- 5.0001)}^{2} - 2 \cdot - 5.0001 - 35}$

Step 1

Evaluate the limit of $\frac{8 (- 5.0001) + 40}{{(- 5.0001)}^{2} - 2 \cdot - 5.0001 - 35}$ which is constant as $x$ approaches $- 5$ .

$\frac{8 (- 5.0001) + 40}{{(- 5.0001)}^{2} - 2 \cdot - 5.0001 - 35}$

Step 2

Simplify the answer.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $8$ by $- 5.0001$ .

$\frac{- 40.0008 + 40}{{(- 5.0001)}^{2} - 2 \cdot - 5.0001 - 35}$

Step 2.1.2

Add $- 40.0008$ and $40$ .

$\frac{- 0.0008}{{(- 5.0001)}^{2} - 2 \cdot - 5.0001 - 35}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Raise $- 5.0001$ to the power of $2$ .

$\frac{- 0.0008}{25.00100001 - 2 \cdot - 5.0001 - 35}$

Step 2.2.2

Multiply $- 2$ by $- 5.0001$ .

$\frac{- 0.0008}{25.00100001 + 10.0002 - 35}$

Step 2.2.3

Add $25.00100001$ and $10.0002$ .

$\frac{- 0.0008}{35.00120001 - 35}$

Step 2.2.4

Subtract $35$ from $35.00120001$ .

$\frac{- 0.0008}{0.00120001}$

Step 2.3

Divide $- 0.0008$ by $0.00120001$ .

$- 0.66666111$