Compute lim f(2+h)-f(2)
h->0 ---------
h
did you mean
Compute lim( f(2+h)-f(2) )/h as h ---> 0 ?
If so, then this has the appearance of attempting to find the derivative of f(x) = x by First Principles when x = 2
Short way is to know that
f ' (x) = 1 , and so the result would be 1
long way:
lim( f(2+h)-f(2) )/h as h ---> 0
= lim ( x + h - x)/h as h --> 0
= lim h/h
= 1
To compute this limit, we need to use the concept of the derivative. The expression you provided is a form of the derivative, known as the definition of the derivative or the difference quotient.
The function f(x) that appears in the formula represents some function we are working with. In order to evaluate the limit, we need to know the specific expression for f(x). Let's assume f(x) = 2x^2 + 3x.
Now, let's substitute the expression for f(x) into the limit:
lim (2 + h)^2 + 3(2 + h) - (2^2 + 3(2))
h->0 ----------------------------------
h
Simplifying this expression will give us the answer.