Calculus Examples

$f (x) = \frac{x^{2} - 25}{x + 5}$

Step 1

Find the domain to determine if the expression is continuous.

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Step 1.1

Set the denominator in $\frac{x^{2} - 25}{x + 5}$ equal to $0$ to find where the expression is undefined.

$x + 5 = 0$

Step 1.2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 1.3

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

Interval Notation:

$(- \infty, - 5) \cup (- 5, \infty)$

Set-Builder Notation:

${x | x \neq - 5}$

Interval Notation:

$(- \infty, - 5) \cup (- 5, \infty)$

Set-Builder Notation:

${x | x \neq - 5}$

Step 2

Since the domain is not all real numbers, $\frac{x^{2} - 25}{x + 5}$ is not continuous over all real numbers.

Not continuous

Step 3

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