Calculus Examples

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

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 $2$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 2

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

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

Step 3

Add $2$ and $2$ .

$\frac{1}{4}$