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Hyperbolic functions

  1. Feb 8, 2012 #1
    1. The problem statement, all variables and given/known data


    Screenshot2012-02-08at22412AM.png

    why is the answer not e^10x ?

    If you ignore the e's it should be

    5x - 5x + 5x - - 5x, or
    5x - 5x + 5x + 5x, which is 10x
     
  2. jcsd
  3. Feb 8, 2012 #2
    If you ignored the e's, it wouldn't be a hyperbolic function, but a linear function.
     
  4. Feb 8, 2012 #3
    well, i still don't see any reason why the answer is not e^10x
     
  5. Feb 8, 2012 #4
    Hint:

    [tex]
    e^{x} + e^{y} \neq e^{x + y}
    [/tex]

    For example: Take [itex]x = y = 0[/itex] and compare the two sides of this unequality.
     
  6. Feb 8, 2012 #5

    Curious3141

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    Homework Helper

    Bob, this is basically [itex]\frac{a+b}{2} + \frac{a-b}{2} = \frac{a}{2} + \frac{b}{2} + \frac{a}{2} - \frac{b}{2} = (2)(\frac{a}{2}) = a[/itex]. Simple algebra. Here [itex]a = e^{5x}[/itex] and [itex]b = e^{-5x}[/itex].

    But your comment indicates a deeper confusion about exponents and algebraic principles. I would suggest that it might be a good idea to review basic algebra including the rules of exponentiation.
     
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