Calculus Examples

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

Step 1

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

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

Step 2

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

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

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Multiply $2$ by $0$ .

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

Step 3.2

Separate fractions.

$\frac{0}{1} \cdot \frac{1}{\tan (x)}$

Step 3.3

Rewrite $\tan (x)$ in terms of sines and cosines.

$\frac{0}{1} \cdot \frac{1}{\frac{\sin (x)}{\cos (x)}}$

Step 3.4

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (x)}{\cos (x)}$ .

$\frac{0}{1} \cdot \frac{\cos (x)}{\sin (x)}$

Step 3.5

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

$\frac{0}{1} \cot (x)$

Step 3.6

Divide $0$ by $1$ .

$0 \cot (x)$

Step 3.7

Multiply $0$ by $\cot (x)$ .

$0$