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Limit as x approaches 2 from the right

  1. Apr 6, 2005 #1
    [itex]
    Lim x->2^+ [Sqrt (x-2)] (1/x-1/2) [/itex]
    Please help im having trouble taking this limit
     
  2. jcsd
  3. Apr 6, 2005 #2

    dextercioby

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    Work on the denominator.Bring that expression to a common denominator and then see whether u can "fix" something with the big fraction's numerator...

    Daniel.
     
  4. Apr 6, 2005 #3

    Hurkyl

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    Just to check, you want:

    [tex]
    \lim_{x \rightarrow 2^+} \sqrt{x-2} \left( \frac{1}{x} - \frac{1}{2} \right)
    [/tex]

    correct?

    What is giving you trouble?
     
  5. Apr 6, 2005 #4
    I simpliefied it to [itex]Lim x->2^+ -Sqrt[x-2]/ 2x [/itex], but that still doesnt help
     
  6. Apr 6, 2005 #5
    yes, when i plug in [itex]2^+[/itex] i can't get a real number
     
  7. Apr 6, 2005 #6

    Hurkyl

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    I don't see the trouble... [itex]\sqrt{2-2}(\frac{1}{2} - \frac{1}{2})[/itex] is a perfectly real number... and there's no issues of domain, because [itex]\sqrt{x-2}[/itex] is defined and continuous on [itex]x \in [2, \infty)[/itex].
     
  8. Apr 6, 2005 #7

    saltydog

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    Huan, I assume you've figured out how to specify a right-handed limit in Mathematica right?

    [tex]Limit[\sqrt{x-2}(\frac{1}{x}-\frac{1}{2}),x\rightarrow 2,Direction\rightarrow -1][/tex]

    This returns 0
     
  9. Apr 6, 2005 #8

    dextercioby

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    Ooops,i was thinking about

    [tex] \lim_{x\searrow 2}\frac{\sqrt{x-2}}{\frac{1}{x}-\frac{1}{2}} [/tex]

    which would have been more interesting...

    Daniel.
     
  10. Apr 6, 2005 #9
    try to use L HOSPİTAL
     
  11. Apr 6, 2005 #10

    dextercioby

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    For what?It's not necessary for mine & it would be incorrect for theirs...

    Daniel.

    EDIT:And one more thing:It's Guillaume François Antoine,marquis de l'Hôpital.
     
    Last edited: Apr 6, 2005
  12. Apr 6, 2005 #11
    are you sure its zero ?
     
  13. Apr 6, 2005 #12
    there is o.o indefiniteness.u can use l hospital
    not:full name is not important
     
  14. Apr 6, 2005 #13

    dextercioby

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    To his limit it's 0 times 0...No indefiniteness.:wink:

    Oh,would you like to be called gursen...?

    Daniel.
     
  15. Apr 6, 2005 #14
    what did you mean by saying 'Oh,would you like to be called gursen...?'
     
  16. Apr 6, 2005 #15

    dextercioby

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    U keep mispelling his name.I wonder if the French dude were still alive & were mis-speling your name,would you have liked it??

    Daniel.
     
  17. Apr 6, 2005 #16
    lan mal i am from turkey
     
  18. Apr 6, 2005 #17

    dextercioby

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    Okay,i'm from Romania,our peoples go way back in the middle ages :wink:

    But still,in modern French,l'Hôpital is l'Hôpital,okay?

    Daniel.
     
  19. Apr 6, 2005 #18
    as i said name is not important.the important thing is the solution
     
  20. Apr 6, 2005 #19
    and however if i said hospital its hospital
     
  21. Apr 6, 2005 #20

    dextercioby

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    Funny,in the XVII-th century French,there was no circumflex accent in writing,so he'd spell his name l'Hospital ...:wink:

    But the French language has evolved...

    Daniel.
     
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