Calculus Examples

$\frac{lim_{x \to 0} \tan (5 x)}{2 x}$

Evaluate the limit.

Tap for more steps...

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

$\frac{\tan (lim_{x \to 0} 5 x)}{2 x}$

Move the term $5$ outside of the limit because it is constant with respect to $x$ .

$\frac{\tan (5 lim_{x \to 0} x)}{2 x}$

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

$\frac{\tan (5 \cdot 0)}{2 x}$

Simplify the answer.

Tap for more steps...

Simplify the numerator.

Tap for more steps...

Multiply $5$ by $0$ .

$\frac{\tan (0)}{2 x}$

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

$\frac{0}{2 x}$

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

Tap for more steps...

Factor $2$ out of $0$ .

$\frac{2 (0)}{2 x}$

Cancel the common factors.

Tap for more steps...

Factor $2$ out of $2 x$ .

$\frac{2 (0)}{2 (x)}$

Cancel the common factor.

$\frac{2 \cdot 0}{2 x}$

Rewrite the expression.

$\frac{0}{x}$

Divide $0$ by $x$ .

$0$