Calculus Examples

$\frac{lim_{x \to 0} 2 x}{\cot (6 x)}$

Step 1

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

$\frac{2 lim_{x \to 0} x}{\cot (6 x)}$

Step 2

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

$\frac{2 \cdot 0}{\cot (6 x)}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $2$ by $0$ .

$\frac{0}{\cot (6 x)}$

Step 3.2

Separate fractions.

$\frac{0}{1} \cdot \frac{1}{\cot (6 x)}$

Step 3.3

Rewrite $\cot (6 x)$ in terms of sines and cosines.

$\frac{0}{1} \cdot \frac{1}{\frac{\cos (6 x)}{\sin (6 x)}}$

Step 3.4

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (6 x)}{\sin (6 x)}$ .

$\frac{0}{1} \cdot \frac{\sin (6 x)}{\cos (6 x)}$

Step 3.5

Convert from $\frac{\sin (6 x)}{\cos (6 x)}$ to $\tan (6 x)$ .

$\frac{0}{1} \tan (6 x)$

Step 3.6

Divide $0$ by $1$ .

$0 \tan (6 x)$

Step 3.7

Multiply $0$ by $\tan (6 x)$ .

$0$