Calculus Examples

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

Step 1

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

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

Step 2

Since the numerator is positive and the denominator $| x + 2 |$ approaches zero and is greater than zero for $x$ near $- 2$ on both sides, the function increases without bound.

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

Step 3

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

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

Step 4

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

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

Step 5

Simplify the answer.

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Step 5.1

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

$\infty + 4$

Step 5.2

Infinity plus or minus a number is infinity.

$\infty$