Calculus Examples

$f (x) = \sqrt{x - 6}$

Step 1

Find the domain to determine if the expression is continuous.

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Step 1.1

Set the radicand in $\sqrt{x - 6}$ greater than or equal to $0$ to find where the expression is defined.

$x - 6 \geq 0$

Step 1.2

Add $6$ to both sides of the inequality.

$x \geq 6$

Step 1.3

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

Interval Notation:

$[6, \infty)$

Set-Builder Notation:

${x | x \geq 6}$

Interval Notation:

$[6, \infty)$

Set-Builder Notation:

${x | x \geq 6}$

Step 2

The expression is continuous.

Continuous

Step 3

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$