Calculus Examples

$\frac{lim_{x \to 0} \sin (x)}{2 x} + 3 x + 4$

Step 1

Move the limit inside the trig function because sine is continuous.

$\frac{\sin (lim_{x \to 0} x)}{2 x} + 3 x + 4$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\frac{\sin (0)}{2 x} + 3 x + 4$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

The exact value of $\sin (0)$ is $0$ .

$\frac{0}{2 x} + 3 x + 4$

Step 3.1.2

Cancel the common factor of $0$ and $2$ .

Tap for more steps...

Step 3.1.2.1

Factor $2$ out of $0$ .

$\frac{2 (0)}{2 x} + 3 x + 4$

Step 3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.2.1

Factor $2$ out of $2 x$ .

$\frac{2 (0)}{2 (x)} + 3 x + 4$

Step 3.1.2.2.2

Cancel the common factor.

$\frac{2 \cdot 0}{2 x} + 3 x + 4$

Step 3.1.2.2.3

Rewrite the expression.

$\frac{0}{x} + 3 x + 4$

Step 3.1.3

Divide $0$ by $x$ .

$0 + 3 x + 4$

Step 3.2

Add $0$ and $3 x$ .

$3 x + 4$