Calculus Examples

$lim_{x \to - 2} \frac{1}{| x |}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{lim_{x \to - 2} 1}{lim_{x \to - 2} | x |}$

Step 1.2

Evaluate the limit of $1$ which is constant as $x$ approaches $- 2$ .

$\frac{1}{lim_{x \to - 2} | x |}$

Step 1.3

Move the limit inside the absolute value signs.

$\frac{1}{| lim_{x \to - 2} x |}$

Step 2

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

$\frac{1}{| - 2 |}$

Step 3

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

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$