Calculus Examples

$lim_{x \to c} (\frac{f (x)}{2 g (x)}) + h (x)$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Cancel the common factor of $f (x)$ and $g (x)$ .

Tap for more steps...

Step 1.1.1

Cancel the common factor.

$lim_{x \to c} \frac{f (x)}{2 g (x)} + h (x)$

Step 1.1.2

Rewrite the expression.

$lim_{x \to c} \frac{1}{2} + h (x)$

Step 1.2

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

$lim_{x \to c} \frac{1}{2} + lim_{x \to c} h (x)$

Step 1.3

Evaluate the limit of $\frac{1}{2}$ which is constant as $x$ approaches $c$ .

$\frac{1}{2} + lim_{x \to c} h (x)$

Step 2

Evaluate the limit of $h (x)$ by plugging in $c$ for $x$ .

$\frac{1}{2} + h (c)$