Calculus Examples

$lim_{x \to 5} | x - 5 |$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the absolute value signs.

$| lim_{x \to 5} x - 5 |$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $5$ .

$| lim_{x \to 5} x - lim_{x \to 5} 5 |$

Step 1.3

Evaluate the limit of $5$ which is constant as $x$ approaches $5$ .

$| lim_{x \to 5} x - 1 \cdot 5 |$

Step 2

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$| 5 - 1 \cdot 5 |$

Step 3

Simplify the answer.

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Step 3.1

Multiply $- 1$ by $5$ .

$| 5 - 5 |$

Step 3.2

Subtract $5$ from $5$ .

$| 0 |$

Step 3.3

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

$0$