Precalculus Examples

$x = 2$

Step 1

Write $x = 2$ as a function.

$f (x) = 2$

Step 2

Consider the difference quotient formula.

$\frac{f (x + h) - f (x)}{h}$

Step 3

Find the components of the definition.

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Step 3.1

Evaluate the function at $x = x + h$ .

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Step 3.1.1

Replace the variable $x$ with $x + h$ in the expression.

$f (x + h) = 2$

Step 3.1.2

The final answer is $2$ .

$2$

$2$

Step 3.2

Find the components of the definition.

$f (x + h) = 2$

$f (x) = 2$

$f (x + h) = 2$

$f (x) = 2$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{2 - (2)}{h}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply $- 1$ by $2$ .

$\frac{2 - 2}{h}$

Step 5.1.2

Subtract $2$ from $2$ .

$\frac{0}{h}$

$\frac{0}{h}$

Step 5.2

Divide $0$ by $h$ .

$0$

$0$

Step 6

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