Calculus Examples

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

Step 1

Change the two-sided limit into a left sided limit.

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

Step 2

Evaluate the limit.

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Step 2.1

Move the limit inside the absolute value signs.

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

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

$| 2 - 1 \cdot 2 |$

Step 4

Simplify the answer.

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Step 4.1

Multiply $- 1$ by $2$ .

$| 2 - 2 |$

Step 4.2

Subtract $2$ from $2$ .

$| 0 |$

Step 4.3

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

$0$