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One-sided limit question

  1. Oct 13, 2014 #1
    1. The problem statement, all variables and given/known data


    Find the ## lim _{x-> -1+} sqrt(x^2-3x)-2/|x+1| ##

    2. Relevant equations


    3. The attempt at a solution

    I can only solve it using l'hopital rule and would like to know the steps of solving it without using it.

    ## lim _{x->-1+} (2x-3)/|1|= -5/4 ##
     
  2. jcsd
  3. Oct 13, 2014 #2

    Mark44

    Staff: Mentor

    Multiply the expression by 1 in the form of the conjugate of the numerator over itself. The |x + 1| factor in the denominator can be replaced by x + 1, since x is to the right of -1, so x + 1 > 0. If the limit had been as x approaches -1 from the left you have to replace |x + 1| by -(x + 1).
     
  4. Oct 13, 2014 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I suppose you mean$$
    \lim_{x\to -1^+}\frac{\sqrt{x^2-3x}-2}{|x+1|}$$which is not what you wrote. Anyway since ##x>-1## you can write ##|x+1|=x+1##. Try rationalizing the numerator and see if you can get it then.

    [Edit] Mark44 must type faster than I do.
     
    Last edited: Oct 13, 2014
  5. Oct 13, 2014 #4
    I'm dumb. Much thanks.
     
  6. Oct 14, 2014 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, you are careless- that, at least, is curable!
     
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