Calculus Examples

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

Step 1

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

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

Step 2

Simplify the answer.

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Step 2.1

Separate fractions.

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

Step 2.2

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

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

Step 2.3

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 2.4

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

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

Step 2.5

Divide $0$ by $1$ .

$0 \cot (x)$

Step 2.6

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

$0$