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Possible proof?

  1. Jan 12, 2010 #1
    possible proof??

    Can we prove that the limit of :

    [tex]lim_{n\to 0}\frac{sinx}{x} =1[/tex]

    By using the ε-δ definition??
     
  2. jcsd
  3. Jan 12, 2010 #2
  4. Jan 13, 2010 #3
    Re: possible proof??

    I don't believe the Squeeze Theorem works too well for this one, because [tex]\lim_{ x \to 0 } \pm \frac{1}{x}[/tex] does not exist. The standard proof of this fact would cite either a geometric argument, Taylor series, or L'Hopital's theorem.
     
  5. Jan 13, 2010 #4
    Re: possible proof??

    i dunno, take the derivative and set x equal to 0 and you get 1. thats proof enough for a physics forum
     
  6. Jan 13, 2010 #5
    Re: possible proof??

    d/dx sin(x) @ x = 0, is defined as: lim x->0 [sin(x) - sin(0)]/x = lim x->0 sin(x)/x.

    Basically, you can't assume that this limit is 1 to prove that this limit is 1, unless ofcourse you can prove that d/dx sin(x) = cos(x) and consider this as a special case (however, you will come to find that hidden in this proof contains the question being asked).
     
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