Calculus Examples

$lim_{x \to - 6} (x + 6) (\frac{| x + 6 |}{x + 6})$

Step 1

Evaluate the limit.

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Step 1.1

Simplify the limit argument.

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Step 1.1.1

Multiply $x + 6$ by $\frac{| x + 6 |}{x + 6}$ .

$lim_{x \to - 6} \frac{(x + 6) | x + 6 |}{x + 6}$

Step 1.1.2

Cancel the common factor of $x + 6$ .

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Step 1.1.2.1

Cancel the common factor.

$lim_{x \to - 6} \frac{(x + 6) | x + 6 |}{x + 6}$

Step 1.1.2.2

Divide $| x + 6 |$ by $1$ .

$lim_{x \to - 6} | x + 6 |$

Step 1.2

Move the limit inside the absolute value signs.

$| lim_{x \to - 6} x + 6 |$

Step 1.3

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

$| lim_{x \to - 6} x + lim_{x \to - 6} 6 |$

Step 1.4

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

$| lim_{x \to - 6} x + 6 |$

Step 2

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

$| - 6 + 6 |$

Step 3

Simplify the answer.

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Step 3.1

Add $- 6$ and $6$ .

$| 0 |$

Step 3.2

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$0$