Calculus Examples

$lim_{x \to 1} \frac{2}{2} \cdot (16 x - 12)$

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.

$lim_{x \to 1} \frac{2}{2} \cdot (16 x - 12)$

Step 1.1.2

Rewrite the expression.

$lim_{x \to 1} 1 \cdot (16 x - 12)$

Step 1.2

Multiply $16 x - 12$ by $1$ .

$lim_{x \to 1} 16 x - 12$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$lim_{x \to 1} 16 x - lim_{x \to 1} 12$

Step 1.4

Move the term $16$ outside of the limit because it is constant with respect to $x$ .

$16 lim_{x \to 1} x - lim_{x \to 1} 12$

Step 1.5

Evaluate the limit of $12$ which is constant as $x$ approaches $1$ .

$16 lim_{x \to 1} x - 1 \cdot 12$

Step 2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$16 \cdot 1 - 1 \cdot 12$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $16$ by $1$ .

$16 - 1 \cdot 12$

Step 3.1.2

Multiply $- 1$ by $12$ .

$16 - 12$

Step 3.2

Subtract $12$ from $16$ .

$4$