Calculus Examples

$lim_{x \to 8} \frac{4}{2} \cdot (8 x - 12)$

Step 1

Evaluate the limit.

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Step 1.1

Cancel the common factor of $4$ and $2$ .

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Step 1.1.1

Factor $2$ out of $4$ .

$lim_{x \to 8} \frac{2 \cdot 2}{2} \cdot (8 x - 12)$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $2$ .

$lim_{x \to 8} \frac{2 \cdot 2}{2 (1)} \cdot (8 x - 12)$

Step 1.1.2.2

Cancel the common factor.

$lim_{x \to 8} \frac{2 \cdot 2}{2 \cdot 1} \cdot (8 x - 12)$

Step 1.1.2.3

Rewrite the expression.

$lim_{x \to 8} \frac{2}{1} \cdot (8 x - 12)$

Step 1.1.2.4

Divide $2$ by $1$ .

$lim_{x \to 8} 2 \cdot (8 x - 12)$

Step 1.2

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to 8} 8 x - 12$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $8$ .

$2 (lim_{x \to 8} 8 x - lim_{x \to 8} 12)$

Step 1.4

Move the term $8$ outside of the limit because it is constant with respect to $x$ .

$2 (8 lim_{x \to 8} x - lim_{x \to 8} 12)$

Step 1.5

Evaluate the limit of $12$ which is constant as $x$ approaches $8$ .

$2 (8 lim_{x \to 8} x - 1 \cdot 12)$

Step 2

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

$2 (8 \cdot 8 - 1 \cdot 12)$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $8$ by $8$ .

$2 (64 - 1 \cdot 12)$

Step 3.1.2

Multiply $- 1$ by $12$ .

$2 (64 - 12)$

Step 3.2

Subtract $12$ from $64$ .

$2 \cdot 52$

Step 3.3

Multiply $2$ by $52$ .

$104$