Calculus Examples

$\frac{lim_{x \to 0} \tan^{2} (3 x)}{2 x}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the exponent $2$ from $\tan^{2} (3 x)$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{x \to 0} \tan (3 x))}^{2}}{2 x}$

Step 1.2

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

$\frac{\tan^{2} (lim_{x \to 0} 3 x)}{2 x}$

Step 1.3

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\frac{\tan^{2} (3 lim_{x \to 0} x)}{2 x}$

Step 2

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

$\frac{\tan^{2} (3 \cdot 0)}{2 x}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Multiply $3$ by $0$ .

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

Step 3.1.2

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

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

Step 3.1.3

Raising $0$ to any positive power yields $0$ .

$\frac{0}{2 x}$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Factor $2$ out of $0$ .

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

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

Factor $2$ out of $2 x$ .

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

$\frac{0}{x}$

Step 3.3

Divide $0$ by $x$ .

$0$