Calculus Examples

$lim_{x \to - 2} \frac{| x |}{x}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $- 2$ .

$\frac{lim_{x \to - 2} | x |}{lim_{x \to - 2} x}$

Step 2

Move the limit inside the absolute value signs.

$\frac{| lim_{x \to - 2} x |}{lim_{x \to - 2} x}$

Step 3

Evaluate the limits by plugging in $- 2$ for all occurrences of $x$ .

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Step 3.1

Evaluate the limit of $x$ by plugging in $- 2$ for $x$ .

$\frac{| - 2 |}{lim_{x \to - 2} x}$

Step 3.2

Evaluate the limit of $x$ by plugging in $- 2$ for $x$ .

$\frac{| - 2 |}{- 2}$

Step 4

Simplify the answer.

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Step 4.1

The absolute value is the distance between a number and zero. The distance between $- 2$ and $0$ is $2$ .

$\frac{2}{- 2}$

Step 4.2

Divide $2$ by $- 2$ .

$- 1$