calculus

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Find the discontinuities of the given function. Classify them as a point discontinuity or a jump discontunuity.

g(x)= x, x<-3
5x/(x^2-4x), x>= -3

  • calculus -

    Evaluate g(x) at points close to the discontinuity:
    Lim x-> -3- g(x) = -3
    g(-3)=5(-3)/((-3)^2-4(-3))
    =-15/21
    =-5/7

    So there is a jump from -3 on the left to -5/7 on the right.

    Can you suggest what kind of discontinuity it is?

  • calculus -

    I assume it's a jump since it jumps from one value to another.

  • calculus -

    That is correct.

    If you do not have clear definitions of each type of discontinuity, you can check the following link:
    http://en.wikipedia.org/wiki/Classification_of_discontinuities

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