Calculus Examples

\frac{lim_{x \to 2} x^{2} - 4}{x - 2}

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

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as

x

$x$ approaches

2

$2$ .

\frac{lim_{x \to 2} x^{2} - lim_{x \to 2} 4}{x - 2}

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

Step 1.2

Move the exponent

2

$2$ from

x^{2}

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

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

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

Step 1.3

Evaluate the limit of

4

$4$ which is constant as

x

$x$ approaches

2

$2$ .

\frac{{(lim_{x \to 2} x)}^{2} - 1 \cdot 4}{x - 2}

$\frac{{(lim_{x \to 2} x)}^{2} - 1 \cdot 4}{x - 2}$

\frac{{(lim_{x \to 2} x)}^{2} - 1 \cdot 4}{x - 2}

$\frac{{(lim_{x \to 2} x)}^{2} - 1 \cdot 4}{x - 2}$

Step 2

Evaluate the limit of

x

$x$ by plugging in

2

$2$ for

x

$x$ .

\frac{2^{2} - 1 \cdot 4}{x - 2}

$\frac{2^{2} - 1 \cdot 4}{x - 2}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise

2

$2$ to the power of

2

$2$ .

\frac{4 - 1 \cdot 4}{x - 2}

$\frac{4 - 1 \cdot 4}{x - 2}$

Step 3.1.2

Multiply

- 1

$- 1$ by

4

$4$ .

\frac{4 - 4}{x - 2}

$\frac{4 - 4}{x - 2}$

Step 3.1.3

Subtract

4

$4$ from

4

$4$ .

\frac{0}{x - 2}

$\frac{0}{x - 2}$

\frac{0}{x - 2}

$\frac{0}{x - 2}$

Step 3.2

Divide

0

$0$ by

x - 2

$x - 2$ .

0

$0$

0

$0$

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

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

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