Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 5$ .

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

Step 1.2

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

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

Step 2

Since the numerator is positive and the denominator $x + 5$ approaches zero and is less than zero for $x$ near $- 5$ to the left, the function decreases without bound.

${(lim_{x \to {(- 5)}^{-}} x)}^{2} + - \infty$

Step 3

Evaluate the limit of $x$ by plugging in $- 5$ for $x$ .

${(- 5)}^{2} + - \infty$

Step 4

Simplify the answer.

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Step 4.1

Raise $- 5$ to the power of $2$ .

$25 + - \infty$

Step 4.2

Infinity plus or minus a number is infinity.

$- \infty$