Precalculus Examples

$f (x) = \sin (\frac{x}{2})$

Step 1

Consider the difference quotient formula.

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

Step 2

Find the components of the definition.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

The final answer is $\sin (\frac{x + h}{2})$ .

$\sin (\frac{x + h}{2})$

Step 2.2

Find the components of the definition.

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

$f (x) = \sin (\frac{x}{2})$

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

$f (x) = \sin (\frac{x}{2})$

Step 3

Plug in the components.

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

Step 4