calculus help: finding f(x) and c from limit formula

[sungjin6458]

the limit represents f'(c) for a function f and a number c. Find f and c.
lim(h->0) [(-2+h)^3 +8]/h
lim(x->0) [(-x^2)+36]/(x-6)
lim(x->9) [2rootx -6]/(x-9)

hi guys i dont understand how to solve these questions. I know they are asking to work backwards and then i don't really get it. i dont think i have to solve out the limit because im supposed to solve backwards. If you can tell me how to solve these questions step by step that'd be great to me to help me understand the concept really well

 

[stapel]

When you set up a limit, you plug an f and a c into the limit formulation, "[f(c + h) - f(c)] / h".

To work backwards, look at the expression they give you. You know that c is added to h, so find the h. Then find what h is added to. So what is c?

You know that "c + h" is plugged in for "x" in the formula for "f(x)". So what is in the parentheses that represents "this is what we plugged c + h into when we plugged c + h in for x in the formula for f(x)"? This gives you the formula for f(x).

Just look at what they give you, and work backwards from the formula you have memorized.

Eliz.

 

[sungjin6458]

so what do you do after you break it down to the formulat? for the 2nd problem i got
f(x+h)=-x^2
f(x)=-36
h=x-6
i guess this is the point ive been stuck all along...
thnx for ur help guys

 

[stapel]

so what do you do after you break it down to the formula?

You write down the formula you've found for f(x) where it asks for "what is f(x)?"

For instance:

. . . . .For lim_h->0 [{(2 + h)³ + 1} - 9] / h, find f(x) and c.

...you would note that h is added to 2, so c = 2. And the parenthetical bit with the 2 + h in it is (2 + h)³ + 1, so f(x) = x³ + 1. Checking, f(2) = 2³ + 1 = 8 + 1 = 9, the bit that's subtracted, which verifies the formula.

Then you write down "f(x) = x³ + 1 and c = 2".

You simply look at it, and work backwards.

Eliz.