Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the term $\frac{1}{t^{2} - 4}$ outside of the limit because it is constant with respect to $x$ .

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

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 2$ .

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

Step 1.3

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

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

Step 2

Evaluate the limit of $x$ by plugging in $- 2$ for $x$ .

$\frac{1}{t^{2} - 4} (- 2 + 2)$

Step 3

Simplify the answer.

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Step 3.1

Simplify the denominator.

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Step 3.1.1

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

$\frac{1}{t^{2} - 2^{2}} (- 2 + 2)$

Step 3.1.2

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 $b = 2$ .

$\frac{1}{(t + 2) (t - 2)} (- 2 + 2)$

Step 3.2

Add $- 2$ and $2$ .

$\frac{1}{(t + 2) (t - 2)} \cdot 0$

Step 3.3

Multiply $\frac{1}{(t + 2) (t - 2)}$ by $0$ .

$0$