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Why does this limit equal 1?

  1. May 6, 2013 #1
    I have a question and here it is :

    [(1/e^x)-1] / [(1/e^x)+1]

    why this equal -1 ?? when X →±∞


    I would appreciate it if you explain it for me on a paper after you capture it by your camera.
     

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    Last edited: May 6, 2013
  2. jcsd
  3. May 6, 2013 #2
    Are you sure the answer is 1? The limit should be -1.
     
  4. May 6, 2013 #3
    sorry I forgot to put the - , yea it does equal -1 but why?
     
  5. May 6, 2013 #4
    What is [tex] \lim_{x\rightarrow \infty} {e^{-x}-1}?[/tex]
    [tex]\lim_{x\rightarrow \infty} {e^{-x}+1} ?[/tex] Just divide these two answers.
     
  6. May 6, 2013 #5

    micromass

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    That only works for the limit to ##+\infty##.
     
  7. May 6, 2013 #6
    yes and that drives me crazy:frown:
     
  8. May 6, 2013 #7
    Thanks, fixed.

    For negative x, multiply the numerator and denominator by [itex] e^x [/itex]
     
  9. May 6, 2013 #8
    so what about when x→-∞ ?
     
  10. May 6, 2013 #9

    micromass

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    First things first. Do you understand the limit when ##x\rightarrow +\infty##?
     
  11. May 6, 2013 #10
    yes I do.
     
  12. May 6, 2013 #11

    micromass

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    Cool. For the other limit, you'll need to follow the hint in #7.

    The answer won't be -1, by the way.
     
  13. May 6, 2013 #12
    I have not seen this after the modification :)



    thanks a lot ,this problem forced me to throw the book away.
     
  14. May 6, 2013 #13

    micromass

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    So you found the right answer??

    Also: you might want to post this in "calculus and beyond" next time :tongue2:
     
  15. May 6, 2013 #14

    yes I got the right answer.

    you must see teachers here in Syria ,they drive you crazy.
    can't wait till I graduate high school and arrive to the US.:wink:
     
  16. May 7, 2013 #15
    actually when I followed hint #7 the answer wasn't -1 ,so Micromass what is the right answer?
     
  17. May 7, 2013 #16
    (e^-x - 1) / (e^-x +1)

    Multiply num and denom by e^x

    (1 - e^x) / (1 + e^x)

    so ya if you got positive 1 with negative infinite that makes sense as that reduces to
    1/1 = 1
     
  18. May 7, 2013 #17
    (1 - e^x) / (1 + e^x) when x→-∞

    yea it does equal 1 , but in my textbook when x→-∞ the equation (e^-x - 1) / (e^-x +1) equal -1 and that make no sense for me.
     
  19. May 7, 2013 #18

    micromass

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    If your textbook says the answer is -1, then your textbook is wrong. The answer is 1.
     
  20. May 7, 2013 #19

    HallsofIvy

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    Are we still talking about "[(1/e^x)-1] / [(1/e^x)+1]" as x goes to infinity? For very large x, 1/e^x is very close to 0 so the fraction is close to -1/1= -1.

    (Oh, I see. The original post said "as [itex]x \to \pm\infty[/itex]" and the limit as x goes to negative infinity is 1.)
     
  21. May 7, 2013 #20

    micromass

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    No, we're talking about the limit to ##-\infty##.
     
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