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

true

explanation:

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.