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Math Help - Continuity of a trig/algibraic function

  1. #1
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    Continuity of a trig/algibraic function

    I have a question in a past paper. Is the following continuous at x=0:
    f(x)= (1-cos(x))/x
    The model answer says no it is not continuous at x=0 and you would have to define f(0)=0 to make it continuous.

    I understand that a/0 is undefined but in this case the numerator is 0 at the same x point that the denominator is thus we have 0/0. Is that still considered undefined and why?

    Thanks
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  2. #2
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    Quote Originally Posted by Rowanmck View Post
    I have a question in a past paper. Is the following continuous at x=0:
    f(x)= (1-cos(x))/x
    The model answer says no it is not continuous at x=0 and you would have to define f(0)=0 to make it continuous.

    I understand that a/0 is undefined but in this case the numerator is 0 at the same x point that the denominator is thus we have 0/0. Is that still considered undefined and why?

    Thanks
    Its still undefined because you're still trying to divide by 0.
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  3. #3
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    Quote Originally Posted by Rowanmck View Post
    I understand that a/0 is undefined but in this case the numerator is 0 at the same x point that the denominator is thus we have 0/0. Is that still considered undefined and why? Thanks
    For ALL numbers a, \dfrac{a}{b} is undefined if b = 0. It doesn't matter whether a = 0 or not.
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  4. #4
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    Thanks for clearing that up for me :-)
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  5. #5
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    L'Hopital's Rule

    L'Hopital's Rule applies here.
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