Calculus Examples

$lim_{r \to - 1} \frac{1}{t^{2} - 1}$

Step 1

Evaluate the limit of $\frac{1}{t^{2} - 1}$ which is constant as $r$ approaches $- 1$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

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 $a = t$ and $b = 1$ .

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