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:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.