Precalculus Examples

$\sin (x)$

Step 1

Write $\sin (x)$ as a function.

$f (x) = \sin (x)$

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.

$f (x + h) = \sin (x + h)$

Step 3.1.2

The final answer is $\sin (x + h)$ .

$\sin (x + h)$

Step 3.2

Find the components of the definition.

$f (x + h) = \sin (x + h)$

$f (x) = \sin (x)$

$f (x + h) = \sin (x + h)$

$f (x) = \sin (x)$

Step 4

Plug in the components.

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

Step 5