Calculus Examples

$\frac{lim_{x \to π} x - π}{2 \tan (3 x)}$

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 $π$ .

$\frac{lim_{x \to π} x - lim_{x \to π} π}{2 \tan (3 x)}$

Step 1.2

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

$\frac{lim_{x \to π} x - π}{2 \tan (3 x)}$

Step 2

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

$\frac{π - π}{2 \tan (3 x)}$

Step 3

Simplify the answer.

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Step 3.1

Subtract $π$ from $π$ .

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

Step 3.2

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

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Step 3.2.1

Factor $2$ out of $0$ .

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

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $2 \tan (3 x)$ .

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

$\frac{0}{\tan (3 x)}$

Step 3.3

Separate fractions.

$\frac{0}{1} \cdot \frac{1}{\tan (3 x)}$

Step 3.4

Rewrite $\tan (3 x)$ in terms of sines and cosines.

$\frac{0}{1} \cdot \frac{1}{\frac{\sin (3 x)}{\cos (3 x)}}$

Step 3.5

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (3 x)}{\cos (3 x)}$ .

$\frac{0}{1} \cdot \frac{\cos (3 x)}{\sin (3 x)}$

Step 3.6

Convert from $\frac{\cos (3 x)}{\sin (3 x)}$ to $\cot (3 x)$ .

$\frac{0}{1} \cot (3 x)$

Step 3.7

Divide $0$ by $1$ .

$0 \cot (3 x)$

Step 3.8

Multiply $0$ by $\cot (3 x)$ .

$0$