Expert: Paul Klarreich - 3/27/2011

Question
If f' is continuous, use l’Hospital’s Rule to show that
lim
x-->0  [f(x+h)-f(x-h)]/2h= f'(x)

Answer
Questioner: lim
Country: Australia
Category: Calculus
Private: Yes   <<<<<<<<<<<<<<<<<<<<<<<<<<<  changed
Subject: calculus
Question: If f' is continuous, use l’Hospital’s Rule to show that
lim
x-->0  [f(x+h)-f(x-h)]/2h= f'(x)
......................................
Of course it isn't.  You did not proofread your question before hitting send.

It is:

lim
h-->0  [f(x+h)-f(x-h)]/2h= f'(x)

Take:

f(x+h) - f(x-h)
----------------
     2h

and differentiate top and bottom WITH RESPECT TO h.  Of course, you will use

the chain rule for the - f(x - h).

Then simplify and let h -> 0.