Calculus Examples

$lim_{x \to - 4} \frac{t + 4}{t^{2} - 16}$

Step 1

Evaluate the limit of $\frac{t + 4}{t^{2} - 16}$ which is constant as $x$ approaches $- 4$ .

$\frac{t + 4}{t^{2} - 16}$

Step 2

Simplify the answer.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

Rewrite $16$ as $4^{2}$ .

$\frac{t + 4}{t^{2} - 4^{2}}$

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 $a = t$ and $b = 4$ .

$\frac{t + 4}{(t + 4) (t - 4)}$

Step 2.2

Cancel the common factor of $t + 4$ .

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Step 2.2.1

Cancel the common factor.

$\frac{t + 4}{(t + 4) (t - 4)}$

Step 2.2.2

Rewrite the expression.

$\frac{1}{t - 4}$