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Calculus Examples

f (x) = \frac{1}{x}

$f (x) = \frac{1}{x}$ ,

[- 6, 6]

$[- 6, 6]$

Step 1

To find whether the function is continuous on

[- 6, 6]

$[- 6, 6]$ or not, find the domain of

f (x) = \frac{1}{x}

$f (x) = \frac{1}{x}$ .

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Step 1.1

Set the denominator in

\frac{1}{x}

$\frac{1}{x}$ equal to

0

$0$ to find where the expression is undefined.

x = 0

$x = 0$

Step 1.2

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

(- \infty, 0) \cup (0, \infty)

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

{x | x \neq 0}

${x | x \neq 0}$

Interval Notation:

(- \infty, 0) \cup (0, \infty)

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

{x | x \neq 0}

${x | x \neq 0}$

Step 2

f (x)

$f (x)$ is not continuous on

[- 6, 6]

$[- 6, 6]$ because

0

$0$ is not in the domain of

f (x) = \frac{1}{x}

$f (x) = \frac{1}{x}$ .

The function is not continuous.

Step 3

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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