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Homework Help: Find the limit

  1. Sep 4, 2008 #1
    1. The problem statement, all variables and given/known data
    2. Find the limit.
    lim
    x->0
    for
    1-sqrt(x^2-1)
    ---------------
    x^2

    2. Relevant equations
    No clue, that's why I am asking.


    3. The attempt at a solution
    I inverted the signs and multiplied by sqrt(x^1+1)+1
    So:
    sqrt(x^2+1)-1 sqrt(x^2+1)+1
    --------------- * --------------
    -(x^2) sqrt(x^2+1)+1
    and came up with
    x+1-1
    ----------------------
    -(x^2)*sqrt(x^2+1)+1
    which gave me
    0/2

    I am sure this isn't correct, but I do not know were I messed up.
     
  2. jcsd
  3. Sep 4, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    (sqrt(x^2+1)-1)*(sqrt(x^2+1)+1)=(x^2+1)-1. Now isn't it? Not (x+1)-1. As (a+b)*(a-b)=a^2-b^2?
     
  4. Sep 5, 2008 #3
    when i graphed it, i found the answer to be
    infinity - infinity*i
    or
    (1-i)*infinity
    none of those answer sound like what a teacher would be looking for, so i would guess the answer is either "limit does not exsist" or you copied the problem wrong
     
  5. Sep 5, 2008 #4

    HallsofIvy

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    Science Advisor

    Your method is perfectly good. You algebra needs some work!
    First you can't just change the x^2- 1 inside the square root into x^2+ 1 by "inverting the sign". Second, (1- sqrt(x^2+ 1))(1+ sqrt(x^2+ 1))= 1- (x^2+11)= -x^2.

    In any case, if you just let x= 0 in the original form, you get (1- i)/0. Since the numerator is not 0, that limit does not exist.
     
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