Calculus Examples

$\frac{lim_{x \to - 2} 5 x}{4 - x^{2}}$

Step 1

Move the term $5$ outside of the limit because it is constant with respect to $x$ .

$\frac{5 lim_{x \to - 2} x}{4 - x^{2}}$

Step 2

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

$\frac{5 \cdot - 2}{4 - x^{2}}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $5$ by $- 2$ .

$\frac{- 10}{4 - x^{2}}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

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

$\frac{- 10}{2^{2} - x^{2}}$

Step 3.2.2

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

$\frac{- 10}{(2 + x) (2 - x)}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{10}{(2 + x) (2 - x)}$