Calculus Examples

$lim_{x \to 9} \frac{{8.9}^{2} - 9 \cdot 8.9}{{8.9}^{2} - 8.9 - 72}$

Step 1

Evaluate the limit of $\frac{{8.9}^{2} - 9 \cdot 8.9}{{8.9}^{2} - 8.9 - 72}$ which is constant as $x$ approaches $9$ .

$\frac{{8.9}^{2} - 9 \cdot 8.9}{{8.9}^{2} - 8.9 - 72}$

Step 2

Simplify the answer.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Raise $8.9$ to the power of $2$ .

$\frac{79.21 - 9 \cdot 8.9}{{8.9}^{2} - 8.9 - 72}$

Step 2.1.2

Multiply $- 9$ by $8.9$ .

$\frac{79.21 - 80.1}{{8.9}^{2} - 8.9 - 72}$

Step 2.1.3

Subtract $80.1$ from $79.21$ .

$\frac{- 0.89}{{8.9}^{2} - 8.9 - 72}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Raise $8.9$ to the power of $2$ .

$\frac{- 0.89}{79.21 - 8.9 - 72}$

Step 2.2.2

Subtract $8.9$ from $79.21$ .

$\frac{- 0.89}{70.31 - 72}$

Step 2.2.3

Subtract $72$ from $70.31$ .

$\frac{- 0.89}{- 1.69}$

Step 2.3

Divide $- 0.89$ by $- 1.69$ .

$0.52662721$