Expert: Paul Klarreich - 12/3/2009

Question
I am having trouble rewriting a function in order to make into the 0/0 or Infinity/Infinity form so L'Hopital rule can be used.

1+x/x - 1-x/x

There is one set of parentheses around the entire function and just 1+x/x subtracted by 1-x/x. I cannot used L'Hopital yet since I get 1/0-1/0 since my limit problem is as x--->0.

Thanks for any help or suggestions.

Answer
Questioner: Alex
Country: United States
Category: Calculus
Private: No
Subject: Rewriting function/fractions so L'Hopital Rule can be applied?
Question: I am having trouble rewriting a function in order to make into the 0/0 or Infinity/Infinity form so L'Hopital rule can be used.

1+x/x - 1-x/x

There is one set of parentheses around the entire function and just 1+x/x subtracted by 1-x/x. I cannot used L'Hopital yet since I get 1/0-1/0 since my limit problem is as x--->0.

Thanks for any help or suggestions.
......................................
I aasume you mean:
            1 + x    1 - x
lim [x-> 0]  ------ - ------
               x       x

You must have a single term to apply l'Hospital's rule (small 'l', and you are required to put an 's' after the 'o' if you can't make that funny French letter).

Now apply the Clint Eastwood rule: [Man's gotta do what a man's gotta do.]

MAKE IT INTO ONE TERM:

            (1 + x) - (1 - x)
lim [x-> 0]  ------------------
                   x


            1 + x - 1 + x
lim [x-> 0]  --------------
                   x

             2x
lim [x-> 0]  --- = 2
              x

You don't even need  l'Hospital's rule at all.