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Simple Limit Problem

  1. Jun 4, 2006 #1
    lim x=>2

    (1/x) - (1/2)
    ------------
    x-2


    I was looking through my notes and found this problem. It shows the answer to be -.25, but I don't see how they got that. I know I want to cancel out the (x-2) on both sides of the division bar, but I'm not sure how to do this. Can anyone help me out? Thanks!
     
  2. jcsd
  3. Jun 4, 2006 #2

    arildno

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    Have you learnt about L'hopital's rule yet?
    If you haven't, let your first step be to write your numerator as a single fraction.
     
  4. Jun 4, 2006 #3

    HallsofIvy

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    L'Hopital's rule is "overkill" here!

    Arildno's second suggestion, writing
    [tex]\frac{1}{x}- \frac{1}{2}[/tex]
    as a single fraction is best. What is the common denominator?
     
  5. Jun 4, 2006 #4
    No, never heard of him, sorry.

    I only see a common numerator of 1 not denominator.

    Can I do this:

    [tex]\frac{-1}{x-2} [/tex] ?
     
    Last edited: Jun 4, 2006
  6. Jun 4, 2006 #5

    arildno

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    HORROR OF HORRORS!!!!!!!!

    NEVER EVER MISTREAT FRACTIONS IN THAT MANNER! :mad: :mad: :mad: :mad:
     
  7. Jun 4, 2006 #6
    umm, OK.

    Can someone else help me out?
     
  8. Jun 4, 2006 #7

    arildno

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    Do you even know what a fraction is, or what the symbol x stands for?
     
  9. Jun 4, 2006 #8
    yes, x is a variable. 1/2 is a fraction.
     
  10. Jun 4, 2006 #9

    arildno

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    No. You have completely misunderstood it.
     
  11. Jun 4, 2006 #10
    Riight. Well, are you going to correct me, or just keep criticizing?
     
  12. Jun 4, 2006 #11

    arildno

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    Why don't you sit back and re-think how we add or subtract fractions together?
     
  13. Jun 4, 2006 #12
    I've been looking at this problem for an hour, I obviously don't know how to do it.
     
  14. Jun 4, 2006 #13

    arildno

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    Look at [itex]\frac{1}{x}-\frac{1}{2}[/itex]
    How many fractions do you have in this expression?
     
  15. Jun 4, 2006 #14
    2 fractions
     
  16. Jun 4, 2006 #15

    arildno

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    Correct!
    Now, what is a common denominator for those fractions?
     
  17. Jun 4, 2006 #16
    -"this message is too short"- 1?
     
  18. Jun 4, 2006 #17
    i'll give you a hint or two
    [tex]\frac{\frac{1}{x} - \frac{1}{2}}{x-2}[/tex]
    [tex]=\frac{\frac{2}{2x} - \frac{x}{2x}}{x-2}[/tex]
    [tex]=\frac{\frac{2-x}{2x}}{x-2}[/tex]
    [tex]=\frac{\frac{-(x-2)}{2x}}{x-2}[/tex]
    [tex]=-\frac{1}{2x}[/tex]
    then substitue x=2 in there to get your answer of -.25
    where i have used the following
    [tex]\frac{\frac{a}{b}}{c}=\frac{a}{bc}[/tex]
    [tex]2-x=-(x-2)[/tex]
    [tex]\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}[/tex]
    [tex]\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}[/tex]
     
    Last edited: Jun 4, 2006
  19. Jun 4, 2006 #18
    Thanks for your help. I'm going to try and soak this in and figure out how u did that.
     
    Last edited: Jun 4, 2006
  20. Jun 4, 2006 #19

    Math Is Hard

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  21. Jun 4, 2006 #20
    yeah you can do that because for example
    [tex]\frac{1\times 2}{2\times 2} = \frac{2}{4}=\frac{1}{2}[/tex]
     
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