Calculus Examples

$lim_{h \to 0} \frac{x^{2} - 1}{x}$

Step 1

Evaluate the limit of $\frac{x^{2} - 1}{x}$ which is constant as $h$ approaches $0$ .

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

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

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

Step 2.2

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 $b = 1$ .

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