Calculus Examples

$lim_{x \to 2} | 4 - x^{2} |$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the absolute value signs.

$| lim_{x \to 2} 4 - x^{2} |$

Step 1.2

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

$| lim_{x \to 2} 4 - lim_{x \to 2} x^{2} |$

Step 1.3

Evaluate the limit of $4$ which is constant as $x$ approaches $2$ .

$| 4 - lim_{x \to 2} x^{2} |$

Step 1.4

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$| 4 - {(lim_{x \to 2} x)}^{2} |$

Step 2

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

$| 4 - 2^{2} |$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Raise $2$ to the power of $2$ .

$| 4 - 1 \cdot 4 |$

Step 3.1.2

Multiply $- 1$ by $4$ .

$| 4 - 4 |$

Step 3.2

Subtract $4$ from $4$ .

$| 0 |$

Step 3.3

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

$0$