Calculus Examples

$\frac{x^{2} + 100}{x}$

Step 1

Write $\frac{x^{2} + 100}{x}$ as an equation.

$y = \frac{x^{2} + 100}{x}$

Step 2

Find the x-intercepts.

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Step 2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{x^{2} + 100}{x}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$x^{2} + 100 = 0$

Step 2.2.2

Solve the equation for $x$ .

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Step 2.2.2.1

Subtract $100$ from both sides of the equation.

$x^{2} = - 100$

Step 2.2.2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 100}$

Step 2.2.2.3

Simplify $\pm \sqrt{- 100}$ .

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Step 2.2.2.3.1

Rewrite $- 100$ as $- 1 (100)$ .

$x = \pm \sqrt{- 1 (100)}$

Step 2.2.2.3.2

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{100}$

Step 2.2.2.3.3

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{100}$

Step 2.2.2.3.4

Rewrite $100$ as $10^{2}$ .

$x = \pm i \cdot \sqrt{10^{2}}$

Step 2.2.2.3.5

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm i \cdot 10$

Step 2.2.2.3.6

Move $10$ to the left of $i$ .

$x = \pm 10 i$

Step 2.2.2.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.2.2.4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 10 i$

Step 2.2.2.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 10 i$

Step 2.2.2.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 10 i, - 10 i$

Step 2.3

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 3

Find the y-intercepts.

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Step 3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{{(0)}^{2} + 100}{0}$

Step 3.2

The equation has an undefined fraction.

Undefined

Step 3.3

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $None$

Step 5