Calculus Examples

$\frac{lim_{x \to 3} f (x) + g (x)}{4 g (x)}$

Step 1

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

$\frac{lim_{x \to 3} f (x) + lim_{x \to 3} g (x)}{4 g (x)}$

Step 2

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

Tap for more steps...

Step 2.1

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

$\frac{f (3) + lim_{x \to 3} g (x)}{4 g (x)}$

Step 2.2

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

$\frac{f (3) + g (3)}{4 g (x)}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Add $f (3)$ and $g (3)$ .

$\frac{2 f (3)}{4 g (x)}$

Step 3.2

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 3.2.1

Factor $2$ out of $2 f (3)$ .

$\frac{2 (f (3))}{4 g (x)}$

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

Factor $2$ out of $4 g (x)$ .

$\frac{2 (f (3))}{2 (2 g (x))}$

Step 3.2.2.2

Cancel the common factor.

$\frac{2 f (3)}{2 (2 g (x))}$

Step 3.2.2.3

Rewrite the expression.

$\frac{f (3)}{2 g (x)}$