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Can anyone guide me for this question?

  1. Sep 20, 2014 #1
    Let f be the function:
    f(x) =
    sin(x) ; x is element of Q
    cos(x) ; x is not element of Q
    Prove, using epsilon-delta definition, that there is a point c,which is element of R at which f is continuous.
    Hint: Consider c such that sin(c) = cos(c); why does such a c exist? Then,
    since you know that sin(x) and cos(x) are continuous at c, for epsilon> 0, you get delta1 >
    0 that gives lsin(x)-sin(c)l <epsilon , and also delta2 > 0 that gives lcos(x)-cos(c)l <epsilon .
    Now, why does delta = min(delta1; delta2) work to show lf(x)- f(c)l < epsilon.
     
  2. jcsd
  3. Sep 20, 2014 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You were given those "hints", right? So where is your work? Have you found c such that sin(c)= cos(c)?

    Why was this posted under "Differential Equations"?
     
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