Calculus Examples

$lim_{x \to - 1} \frac{- {1.01}^{2} - 7 \cdot - 1.01}{- {1.01}^{2} - 6 \cdot - 1.01 - 7}$

Step 1

Evaluate the limit of $\frac{- {1.01}^{2} - 7 \cdot - 1.01}{- {1.01}^{2} - 6 \cdot - 1.01 - 7}$ which is constant as $x$ approaches $- 1$ .

$\frac{- {1.01}^{2} - 7 \cdot - 1.01}{- {1.01}^{2} - 6 \cdot - 1.01 - 7}$

Step 2

Simplify the answer.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Raise $1.01$ to the power of $2$ .

$\frac{- 1 \cdot 1.0201 - 7 \cdot - 1.01}{- {1.01}^{2} - 6 \cdot - 1.01 - 7}$

Step 2.1.2

Multiply $- 1$ by $1.0201$ .

$\frac{- 1.0201 - 7 \cdot - 1.01}{- {1.01}^{2} - 6 \cdot - 1.01 - 7}$

Step 2.1.3

Multiply $- 7$ by $- 1.01$ .

$\frac{- 1.0201 + 7.07}{- {1.01}^{2} - 6 \cdot - 1.01 - 7}$

Step 2.1.4

Add $- 1.0201$ and $7.07$ .

$\frac{6.0499}{- {1.01}^{2} - 6 \cdot - 1.01 - 7}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Raise $1.01$ to the power of $2$ .

$\frac{6.0499}{- 1 \cdot 1.0201 - 6 \cdot - 1.01 - 7}$

Step 2.2.2

Multiply $- 1$ by $1.0201$ .

$\frac{6.0499}{- 1.0201 - 6 \cdot - 1.01 - 7}$

Step 2.2.3

Multiply $- 6$ by $- 1.01$ .

$\frac{6.0499}{- 1.0201 + 6.06 - 7}$

Step 2.2.4

Add $- 1.0201$ and $6.06$ .

$\frac{6.0499}{5.0399 - 7}$

Step 2.2.5

Subtract $7$ from $5.0399$ .

$\frac{6.0499}{- 1.9601}$

Step 2.3

Divide $6.0499$ by $- 1.9601$ .

$- 3.08652619$