Calculus Examples

$lim_{x \to - 2} \frac{1}{x + 3}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{lim_{x \to - 2} 1}{lim_{x \to - 2} x + 3}$

Step 1.2

Evaluate the limit of $1$ which is constant as $x$ approaches $- 2$ .

$\frac{1}{lim_{x \to - 2} x + 3}$

Step 1.3

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

$\frac{1}{lim_{x \to - 2} x + lim_{x \to - 2} 3}$

Step 1.4

Evaluate the limit of $3$ which is constant as $x$ approaches $- 2$ .

$\frac{1}{lim_{x \to - 2} x + 3}$

Step 2

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

$\frac{1}{- 2 + 3}$

Step 3

Simplify the answer.

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Step 3.1

Add $- 2$ and $3$ .

$\frac{1}{1}$

Step 3.2

Divide $1$ by $1$ .

$1$