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X-tanh ax = 0

  1. Apr 18, 2012 #1
    Can anybody help me with this equation?

    I need answer for the question, how many real solutions does the equation x-tanh ax = 0 have for a>1?
     
  2. jcsd
  3. Apr 18, 2012 #2

    tiny-tim

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    welcome to pf!

    hi physicsblr! welcome to pf! :smile:

    draw the graph, for 0 ≤ x ≤ 1 (since tanh can't be ≥ 1) …

    what is the slope of tanhax ? :wink:
     
  4. Apr 18, 2012 #3
    Is it a?
     
  5. Apr 18, 2012 #4
    I have a doubt. x=0 is a root of this eq and since its a linear eq, it has only 1 root?
     
  6. Apr 18, 2012 #5

    tiny-tim

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    no, of course not :redface:

    how do we find the slope of a graph?​
     
  7. Apr 18, 2012 #6
    oh! slope is zero.
     
  8. Apr 18, 2012 #7

    tiny-tim

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    how do we find the slope of a graph?
     
  9. Apr 18, 2012 #8
    first derivative of the equation = 0 gives the slope.
     
  10. Apr 18, 2012 #9

    tiny-tim

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    well, first derivative of the equation gives the slope

    so the slope of tanhax is … ? :smile:
     
  11. Apr 19, 2012 #10
    1-tanh2 ax; so for that eq. tanh2 ax = 0 is final result.
     
  12. Apr 19, 2012 #11

    tiny-tim

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    (try using the X2 button just above the Reply box :wink:)
    (= sech2ax)

    no

    use the chain rule​
     
  13. Apr 19, 2012 #12
    am getting 2 cases. either a=1 or sech2 ax=1.
     
  14. Apr 19, 2012 #13

    tiny-tim

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    uhh? :redface:

    what question are you answering? :confused:

    (and you still need to find the correct derivative of tanh(ax))
     
  15. Apr 20, 2012 #14
    Am unable to get it properly, am no good in mathematics. If u can pls explain it and give an answer since I have an entrance exam next week, I will be very thankful.
     
  16. Apr 20, 2012 #15

    tiny-tim

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    i] draw the graph of y = x for 0≤x≤1 …

    that'll be a square with a diagonal​

    ii] find the derivative of y = tanh(ax)

    (that is not sech2(ax) … do it again, using the chain rule)

    iii] the derivative equals the slope of the graph of y = tanh(ax), so plot the values at x = 0 and 1, and use the slope to find how it starts and finishes …

    what do you get? :smile:
     
  17. Apr 20, 2012 #16
    When x=0, y=1 and there on as x is increasing, value of y is decreasing..
     
  18. Apr 20, 2012 #17

    tiny-tim

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    uhh? :confused:

    what was unclear about? …
     
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