Calculus Examples

$\tan (2 x)$

Step 1

Set the argument in

$\tan (2 x)$ equal to

$\frac{π}{2} + π n$ to find where the expression is undefined.

$2 x = \frac{π}{2} + π n$ , for any integer

$n$

Step 2

Divide each term in

$2 x = \frac{π}{2} + π n$ by

$2$ and simplify.

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Step 2.1

Divide each term in

$2 x = \frac{π}{2} + π n$ by

$2$ .

$\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{π n}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

$2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{π n}{2}$

Step 2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{\frac{π}{2}}{2} + \frac{π n}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{π}{2} \cdot \frac{1}{2} + \frac{π n}{2}$

Step 2.3.1.2

Multiply

$\frac{π}{2} \cdot \frac{1}{2}$ .

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Step 2.3.1.2.1

Multiply

$\frac{π}{2}$ by

$\frac{1}{2}$ .

$x = \frac{π}{2 \cdot 2} + \frac{π n}{2}$

Step 2.3.1.2.2

Multiply

$2$ by

$2$ .

$x = \frac{π}{4} + \frac{π n}{2}$

Step 3

The equation is undefined where the denominator equals

$0$ , the argument of a square root is less than

$0$ , or the argument of a logarithm is less than or equal to

$0$ .

${x | x = \frac{π}{4} + \frac{π n}{2}}$

$n$ , for any integer

$n$

Step 4