Calculus Examples

$\frac{lim_{x \to 0} \sin (4 x)}{5 x}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

$\frac{\sin (lim_{x \to 0} 4 x)}{5 x}$

Step 1.2

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$\frac{\sin (4 lim_{x \to 0} x)}{5 x}$

Step 2

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

$\frac{\sin (4 \cdot 0)}{5 x}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Multiply $4$ by $0$ .

$\frac{\sin (0)}{5 x}$

Step 3.1.2

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

$\frac{0}{5 x}$

Step 3.2

Cancel the common factor of $0$ and $5$ .

Tap for more steps...

Step 3.2.1

Factor $5$ out of $0$ .

$\frac{5 (0)}{5 x}$

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

Factor $5$ out of $5 x$ .

$\frac{5 (0)}{5 (x)}$

Step 3.2.2.2

Cancel the common factor.

$\frac{5 \cdot 0}{5 x}$

Step 3.2.2.3

Rewrite the expression.

$\frac{0}{x}$

Step 3.3

Divide $0$ by $x$ .

$0$