Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Simplify the expression.

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Step 5.1

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

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

Step 5.2

Add $2$ and $2$ .

$\frac{1}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$