If f(x)=x^3-9,find lim f(x+h)-f(x)/h
h>0

Hi! Your answer is 3x²

Please read an explanation for a clear understanding to the problem.

Any questions about the answer/explanation can be asked through comments! :)

Step-by-step explanation:

Goal

Given

Step 1

Since f(x) = x³-9. Therefore, f(x+h) would be (x+h)³-9

Simplify the numerator

Step 2

When finding a limit of function, we can't let the approaching variable equal to 0 (Unless if a function doesn't really have limits.)

Cancel both h-term from denominator and numerator

Step 3

Since we can't proceed anymore, therefore. The answer is 3x²

Additional Information

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length

nswer: a   y-axis

step-by-step explanation: