Calculus Examples

$f (x) = \csc (9 x)$

Step 1

Set the argument in $\csc (9 x)$ equal to $π n$ to find where the expression is undefined.

$9 x = π n$ , for any integer $n$

Step 2

Divide each term in $9 x = π n$ by $9$ and simplify.

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Step 2.1

Divide each term in $9 x = π n$ by $9$ .

$\frac{9 x}{9} = \frac{π n}{9}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{π n}{9}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{π n}{9}$

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 $0$ .

${x | x = \frac{π n}{9}}$ $n$ , for any integer $n$

Step 4