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Homework Help: Limits and substituting pi/14

  1. Sep 24, 2008 #1
    1. The problem statement, all variables and given/known data

    http://i38.tinypic.com/v6m1bo.png

    2. Relevant equations



    3. The attempt at a solution

    I tried substituting pi/14 it doesnt accept that answer.
     
  2. jcsd
  3. Sep 24, 2008 #2

    Dick

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    Re: limits

    7*pi/14=pi/2. What's the behavior of tan(x) like as x->pi/2 from above?
     
  4. Sep 24, 2008 #3
    Re: limits

    it gets close to 1.57~
     
  5. Sep 24, 2008 #4

    Dick

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    Re: limits

    7*x gets close to pi/2=1.57~, as x->(pi/14)+, sure. But x->(pi/14)+ means thinking of x's a little larger than pi/14. What's tan(7*(pi/14+0.01)), tan(7*(pi/14+0.001)) etc etc. Punch them into a calculator if you have to.
     
  6. Sep 24, 2008 #5
    Re: limits

    tan(7 ( pi / 14 +.01 ) ) is .028645
    tan(7 ( pi / 14 +.001 ) ) is .027545
    tan(7 ( pi / 14 +.0001 ) ) is .027435
    tan(7 ( pi / 14 +.00001 ) ) is .027424

    so basically, its approaching .02742
     
  7. Sep 24, 2008 #6

    Dick

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    Re: limits

    I get tan(7*((pi/14)+0.001))=-1428.57... Are you using an bad approximation of pi? Don't. 7*pi/14+(a small number) is pi/2+(a small number). What's tan(pi/2+(a small number))? Look at a graph of tan.
     
  8. Sep 24, 2008 #7
    Re: limits

    I got -999.9996667 for tan(pi/2+.001)

    my calculator was in degrees. ;O
     
  9. Sep 24, 2008 #8

    Dick

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    Re: limits

    I forgot about that way of making a mistake. Good for you for catching it. Now if 0.001 gets even smaller??
     
  10. Sep 24, 2008 #9
    Re: limits

    .0001 ~-9999.999967

    but when I use .00001 my calculator rounds to -100000 but it should be around -99999.9999967

    right?
     
  11. Sep 24, 2008 #10

    Dick

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    Re: limits

    Sure, sure. But the point is that tan(7x) is going to minus infinity as x->(pi/14)+, right? Again look at a graph of tan(x) just above pi/2. Agreed?
     
  12. Sep 24, 2008 #11
    Re: limits

    Yes, I see it is approaching minus infinity, I can also see it on the graph as well.
     
  13. Sep 24, 2008 #12

    Dick

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    Re: limits

    Good, good. So what does e^(tan(7*x)) approach?
     
  14. Sep 24, 2008 #13
    Re: limits

    negative infinity?
     
  15. Sep 24, 2008 #14

    Dick

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    Re: limits

    tan(7x) approaches negative infinity. What's, oh, say e^(-100000000)? If your calculator overflows, try e^(-100).
     
  16. Sep 24, 2008 #15
    Re: limits

    0.

    as the number decreases, x approaches 0.

    so the limit would be 0?
     
  17. Sep 24, 2008 #16

    Dick

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    Re: limits

    You said it, not me. But x doesn't approach 0. e^tan(7*x) approaches 0 as x->(pi/14)+. Sure, 0.
     
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