Calculus Examples

$lim_{x \to 5} \frac{1}{x - 2}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $5$ .

$\frac{lim_{x \to 5} 1}{lim_{x \to 5} x - 2}$

Step 1.2

Evaluate the limit of $1$ which is constant as $x$ approaches $5$ .

$\frac{1}{lim_{x \to 5} x - 2}$

Step 1.3

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

$\frac{1}{lim_{x \to 5} x - lim_{x \to 5} 2}$

Step 1.4

Evaluate the limit of $2$ which is constant as $x$ approaches $5$ .

$\frac{1}{lim_{x \to 5} x - 1 \cdot 2}$

Step 2

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

$\frac{1}{5 - 1 \cdot 2}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Multiply $- 1$ by $2$ .

$\frac{1}{5 - 2}$

Step 3.2

Subtract $2$ from $5$ .

$\frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$