Calculus Examples

$lim_{x \to 10} | - x - 5 |$

Step 1

Move the limit inside the absolute value signs.

$| lim_{x \to 10} - x - 5 |$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $10$ .

$| - lim_{x \to 10} x - lim_{x \to 10} 5 |$

Step 3

Evaluate the limit of $5$ which is constant as $x$ approaches $10$ .

$| - lim_{x \to 10} x - 1 \cdot 5 |$

Step 4

Simplify terms.

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Step 4.1

Evaluate the limit of $x$ by plugging in $10$ for $x$ .

$| - 10 - 1 \cdot 5 |$

Step 4.2

Simplify the answer.

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Step 4.2.1

Multiply $- 1$ by $5$ .

$| - 10 - 5 |$

Step 4.2.2

Subtract $5$ from $- 10$ .

$| - 15 |$

Step 4.2.3

The absolute value is the distance between a number and zero. The distance between $- 15$ and $0$ is $15$ .

$15$