Calculus Examples

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

Step 1

Move the limit inside the absolute value signs.

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify terms.

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Step 4.1

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

$\frac{| 5 - 5 |}{5 - x}$

Step 4.2

Simplify the answer.

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Step 4.2.1

Simplify the numerator.

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Step 4.2.1.1

Subtract $5$ from $5$ .

$\frac{| 0 |}{5 - x}$

Step 4.2.1.2

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

$\frac{0}{5 - x}$

Step 4.2.2

Divide $0$ by $5 - x$ .

$0$