Precalculus Examples

Find the Average Rate of Change f(x)=( square root of x^2-1)/x , 1<=x<=7
,
Step 1
Write as an equation.
Step 2
Substitute using the average rate of change formula.
Tap for more steps...
Step 2.1
The average rate of change of a function can be found by calculating the change in values of the two points divided by the change in values of the two points.
Step 2.2
Substitute the equation for and , replacing in the function with the corresponding value.
Step 3
Simplify the expression.
Tap for more steps...
Step 3.1
Divide by .
Step 3.2
Multiply the numerator and denominator of the fraction by .
Tap for more steps...
Step 3.2.1
Multiply by .
Step 3.2.2
Combine.
Step 3.3
Apply the distributive property.
Step 3.4
Cancel the common factor of .
Tap for more steps...
Step 3.4.1
Cancel the common factor.
Step 3.4.2
Rewrite the expression.
Step 3.5
Simplify the numerator.
Tap for more steps...
Step 3.5.1
Raise to the power of .
Step 3.5.2
Subtract from .
Step 3.5.3
Rewrite as .
Tap for more steps...
Step 3.5.3.1
Factor out of .
Step 3.5.3.2
Rewrite as .
Step 3.5.4
Pull terms out from under the radical.
Step 3.5.5
One to any power is one.
Step 3.5.6
Subtract from .
Step 3.5.7
Rewrite as .
Step 3.5.8
Pull terms out from under the radical, assuming positive real numbers.
Step 3.5.9
Multiply .
Tap for more steps...
Step 3.5.9.1
Multiply by .
Step 3.5.9.2
Multiply by .
Step 3.5.10
Add and .
Step 3.6
Simplify the denominator.
Tap for more steps...
Step 3.6.1
Multiply by .
Step 3.6.2
Multiply .
Tap for more steps...
Step 3.6.2.1
Multiply by .
Step 3.6.2.2
Multiply by .
Step 3.6.3
Subtract from .
Step 3.7
Cancel the common factor of and .
Tap for more steps...
Step 3.7.1
Factor out of .
Step 3.7.2
Cancel the common factors.
Tap for more steps...
Step 3.7.2.1
Factor out of .
Step 3.7.2.2
Cancel the common factor.
Step 3.7.2.3
Rewrite the expression.
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: