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Math Help - continuity

  1. #1
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    continuity

    discuss the continuity of function f(x)=(3*x-mod(x))/5*x) x(not equal)=0
    =4 x=0

    i think function is discontinuous at x=0
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: continuity

    Express f(x)=\begin{Bmatrix}{ 2/5}&\mbox{ if }& x>0 \\4 & \mbox{if}& x=0\\ 4/5 & \mbox{if}& x<0\end{matrix}

    Conclude.
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  3. #3
    MHF Contributor chisigma's Avatar
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    Re: continuity

    Quote Originally Posted by prasum View Post
    discuss the continuity of function f(x)=(3*x-mod(x))/5*x) x(not equal)=0
    =4 x=0

    i think function is discontinuous at x=0
    Is...

    \lim_{x \rightarrow 0+} f(x) = \frac{2}{5}

    \lim_{x \rightarrow 0-} f(x) = \frac{4}{5}

    ... so that, independently from the value of f(x) in x=0, only one conclusion is possible...
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