Calculus Examples

$lim_{x \to 5} - \frac{2}{2} \cdot (12 x - 8)$

Step 1

Evaluate the limit.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Cancel the common factor.

$lim_{x \to 5} - \frac{2}{2} \cdot (12 x - 8)$

Step 1.1.2

Rewrite the expression.

$lim_{x \to 5} - 1 \cdot 1 \cdot (12 x - 8)$

Step 1.2

Multiply $- 1$ by $1$ .

$lim_{x \to 5} - 1 \cdot (12 x - 8)$

Step 1.3

Move the term $- 1$ outside of the limit because it is constant with respect to $x$ .

$- lim_{x \to 5} 12 x - 8$

Step 1.4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $5$ .

$- (lim_{x \to 5} 12 x - lim_{x \to 5} 8)$

Step 1.5

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$- (12 lim_{x \to 5} x - lim_{x \to 5} 8)$

Step 1.6

Evaluate the limit of $8$ which is constant as $x$ approaches $5$ .

$- (12 lim_{x \to 5} x - 1 \cdot 8)$

Step 2

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$- (12 \cdot 5 - 1 \cdot 8)$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $12$ by $5$ .

$- (60 - 1 \cdot 8)$

Step 3.1.2

Multiply $- 1$ by $8$ .

$- (60 - 8)$

Step 3.2

Subtract $8$ from $60$ .

$- 1 \cdot 52$

Step 3.3

Multiply $- 1$ by $52$ .

$- 52$