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Homework Help: Continuity With Piece Wise Functions

  1. Oct 6, 2015 #1
    1. The problem statement, all variables and given/known data
    Determine all values of the constant a such that the following function is continuous for all real numbers.
    f(x) = ax/tan(x), x ≥ 0
    = a2 - 2, x < 0
    2. Relevant equations

    3. The attempt at a solution
    I tried so many different ways to get the first part of the function to be defined at 0 but nothing worked, I tried manipulating it with a bunch of trig identities and no matter what, that first part is always undefined at 0 so I don't know how the function can ever be continuous if that first part of the function is always going to be undefined at 0 and I can't remove it.
  2. jcsd
  3. Oct 6, 2015 #2


    Staff: Mentor

    This limit will be helpful:
    $$\lim_{x \to 0} \frac {\sin x} x = 1$$

    Note that ##\frac{ax}{\tan(x)} = a \frac x {\frac{\sin(x)}{\cos(x)}}##
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