Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the absolute value signs.

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

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

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

Step 1.3

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

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

Step 2

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

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

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $- 1$ by $2$ .

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

Step 3.1.2

Subtract $2$ from $2$ .

$\frac{| 0 |}{x - 2}$

Step 3.1.3

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

$\frac{0}{x - 2}$

Step 3.2

Divide $0$ by $x - 2$ .

$0$