Calculus Examples

$lim_{x \to 3} \frac{x + 9}{5 - x}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $3$ .

$\frac{lim_{x \to 3} x + 9}{lim_{x \to 3} 5 - x}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $3$ .

$\frac{lim_{x \to 3} x + lim_{x \to 3} 9}{lim_{x \to 3} 5 - x}$

Step 3

Evaluate the limit of $9$ which is constant as $x$ approaches $3$ .

$\frac{lim_{x \to 3} x + 9}{lim_{x \to 3} 5 - x}$

Step 4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $3$ .

$\frac{lim_{x \to 3} x + 9}{lim_{x \to 3} 5 - lim_{x \to 3} x}$

Step 5

Evaluate the limit of $5$ which is constant as $x$ approaches $3$ .

$\frac{lim_{x \to 3} x + 9}{5 - lim_{x \to 3} x}$

Step 6

Evaluate the limits by plugging in $3$ for all occurrences of $x$ .

Tap for more steps...

Step 6.1

Evaluate the limit of $x$ by plugging in $3$ for $x$ .

$\frac{3 + 9}{5 - lim_{x \to 3} x}$

Step 6.2

Evaluate the limit of $x$ by plugging in $3$ for $x$ .

$\frac{3 + 9}{5 - 3}$

Step 7

Simplify the answer.

Tap for more steps...

Step 7.1

Add $3$ and $9$ .

$\frac{12}{5 - 3}$

Step 7.2

Subtract $3$ from $5$ .

$\frac{12}{2}$

Step 7.3

Divide $12$ by $2$ .

$6$