Calculus Examples

$lim_{x \to - 8} \frac{12 x^{3}}{3000 x^{2}}$

Step 1

Reduce.

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Step 1.1

Cancel the common factor of $12$ and $3000$ .

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Step 1.1.1

Factor $12$ out of $12 x^{3}$ .

$lim_{x \to - 8} \frac{12 (x^{3})}{3000 x^{2}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $12$ out of $3000 x^{2}$ .

$lim_{x \to - 8} \frac{12 (x^{3})}{12 (250 x^{2})}$

Step 1.1.2.2

Cancel the common factor.

$lim_{x \to - 8} \frac{12 x^{3}}{12 (250 x^{2})}$

Step 1.1.2.3

Rewrite the expression.

$lim_{x \to - 8} \frac{x^{3}}{250 x^{2}}$

Step 1.2

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 1.2.1

Factor $x^{2}$ out of $x^{3}$ .

$lim_{x \to - 8} \frac{x^{2} x}{250 x^{2}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $x^{2}$ out of $250 x^{2}$ .

$lim_{x \to - 8} \frac{x^{2} x}{x^{2} \cdot 250}$

Step 1.2.2.2

Cancel the common factor.

$lim_{x \to - 8} \frac{x^{2} x}{x^{2} \cdot 250}$

Step 1.2.2.3

Rewrite the expression.

$lim_{x \to - 8} \frac{x}{250}$

Step 2

Move the term $\frac{1}{250}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{250} lim_{x \to - 8} x$

Step 3

Evaluate the limit of $x$ by plugging in $- 8$ for $x$ .

$\frac{1}{250} \cdot - 8$

Step 4

Simplify the answer.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $250$ .

$\frac{1}{2 (125)} \cdot - 8$

Step 4.1.2

Factor $2$ out of $- 8$ .

$\frac{1}{2 \cdot 125} \cdot (2 \cdot - 4)$

Step 4.1.3

Cancel the common factor.

$\frac{1}{2 \cdot 125} \cdot (2 \cdot - 4)$

Step 4.1.4

Rewrite the expression.

$\frac{1}{125} \cdot - 4$

Step 4.2

Combine $\frac{1}{125}$ and $- 4$ .

$\frac{- 4}{125}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{4}{125}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{125}$

Decimal Form:

$- 0.032$