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Math Help - Continuous on a range

  1. #1
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    Continuous on a range

    Hi i need help with problem 36.
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Continuous on a range

    sin(x) is a continous function, cos(x) is a continous function, so you only need to verify that at  x = \frac{\pi}{4} ,  sin(\frac{\pi}{4}) = cos(\frac{\pi}{4}) . Why is this? Basically even though  \frac{\pi}{4} is not in the domain of sin(x),  lim_{x^{-} \to \frac{\pi}{4}} f(x) \to cos(\frac{\pi}{4})  lim_{x^{-} \to \frac{\pi}{4}} f(x) = lim_{x^{-} \to \frac{\pi}{4}} sin(x) Since sin(x) is continous  lim_{x^{-} \to \frac{\pi}{4}} sin(x) = sin(\frac{\pi}{4})

    In a gist, if you come at  x = \frac{\pi}{4} from the left, it should be the same as if you come at it from the right. The only point at which problem can arise is at  x = \frac{\pi}{4} , which is why you need to check there.
    Last edited by jakncoke; February 8th 2013 at 10:40 AM.
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