Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

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

Step 1.2

Evaluate the limit of $2$ which is constant as $x$ approaches $0$ .

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

Step 2

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

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

Step 3

Simplify the answer.

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Step 3.1

Add $0$ and $2$ .

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

Step 3.2

Separate fractions.

$\frac{2}{1} \cdot \frac{1}{\cot (x)}$

Step 3.3

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

$\frac{2}{1} \cdot \frac{1}{\frac{\cos (x)}{\sin (x)}}$

Step 3.4

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

$\frac{2}{1} \cdot \frac{\sin (x)}{\cos (x)}$

Step 3.5

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

$\frac{2}{1} \tan (x)$

Step 3.6

Divide $2$ by $1$ .

$2 \tan (x)$