Calculus Examples

$lim_{x \to 4} x - | x |$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$lim_{x \to 4} x - lim_{x \to 4} | x |$

Step 2

Move the limit inside the absolute value signs.

$lim_{x \to 4} x - | lim_{x \to 4} x |$

Step 3

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 3.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4 - | lim_{x \to 4} x |$

Step 3.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4 - | 4 |$

Step 4

Simplify the answer.

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Step 4.1

Simplify each term.

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Step 4.1.1

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$4 - 1 \cdot 4$

Step 4.1.2

Multiply $- 1$ by $4$ .

$4 - 4$

Step 4.2

Subtract $4$ from $4$ .

$0$