Calculus Examples

$f (x) = 2 \cot (x + \frac{π}{2})$

Step 1

Set the argument in $\cot (x + \frac{π}{2})$ equal to $π n$ to find where the expression is undefined.

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

Step 2

Subtract $\frac{π}{2}$ from both sides of the equation.

$x = π n - \frac{π}{2}$

Step 3

The domain is all values of $x$ that make the expression defined.

Set-Builder Notation:

${x | x \neq π n - \frac{π}{2}}$ , for any integer $n$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain: ${x | x \neq π n - \frac{π}{2}}$ , for any integer $n$

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6