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

i can't see the picture : /