Calculus Examples

$\frac{lim_{x \to - 6} 2 x + 12}{| x + 6 |}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 6$ .

$\frac{lim_{x \to - 6} 2 x + lim_{x \to - 6} 12}{| x + 6 |}$

Step 1.2

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

$\frac{2 lim_{x \to - 6} x + lim_{x \to - 6} 12}{| x + 6 |}$

Step 1.3

Evaluate the limit of $12$ which is constant as $x$ approaches $- 6$ .

$\frac{2 lim_{x \to - 6} x + 12}{| x + 6 |}$

Step 2

Evaluate the limit of $x$ by plugging in $- 6$ for $x$ .

$\frac{2 \cdot - 6 + 12}{| x + 6 |}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $2$ by $- 6$ .

$\frac{- 12 + 12}{| x + 6 |}$

Step 3.1.2

Add $- 12$ and $12$ .

$\frac{0}{| x + 6 |}$

Step 3.2

Divide $0$ by $| x + 6 |$ .

$0$