Calculus Examples

$lim_{x \to 2} 1 = \frac{x^{2} - 4}{x - 2}$

Step 1

Evaluate the limit of $1$ which is constant as $x$ approaches $2$ .

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

Step 2

Simplify the answer.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Rewrite $4$ as $2^{2}$ .

$1 = \frac{x^{2} - 2^{2}}{x - 2}$

Step 2.1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$1 = \frac{(x + 2) (x - 2)}{x - 2}$

Step 2.2

Cancel the common factor of $x - 2$ .

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Step 2.2.1

Cancel the common factor.

$1 = \frac{(x + 2) (x - 2)}{x - 2}$

Step 2.2.2

Divide $x + 2$ by $1$ .

$1 = x + 2$