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Math Help - Discontinuities

  1. #1
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    Red face Discontinuities

    Could someone help me on this assignment question.

    F(x)= -x+b, if x<2
    1, if x=2
    (-4/(x-b))-3, if x>2(and x cannot equal b)

    For what value(s) of b does f have a removable discontinuity at 2?


    For what value(s) of b does g have an infinite discontinuity at 2?

    For what value(s) of b does f have a (finite) jump discontinuity at 2 in interval notation.
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  2. #2
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    Quote Originally Posted by ctran View Post
    Could someone help me on this assignment question.

    F(x)= -x+b, if x<2
    1, if x=2
    (-4/(x-b))-3, if x>2(and x cannot equal b)

    For what value(s) of b does f have a removable discontinuity at 2?

    For what value(s) of b does g have an infinite discontinuity at 2?

    For what value(s) of b does f have a (finite) jump discontinuity at 2 in interval notation.
    Things that are worthwhile knowing to solve this exercise:

    == lim f(x) when x --> x_o exists iff both one-sided limits exist and they're identical

    == x = a is a removable discontinuity of function f if f(a) exists and also limf(x) when x --> a exists and finite, but they aren't equal

    I'm not sure what you guys call "an infinite discontinuity" to, but if it refers to a point a s.t. lim f(x) when x --> a from the right or from the left (or from both) is oo or -oo, then...well, calculate the limits.

    == jump discontinuity is when both one-sided limits exist finitely both they're different.

    Now do some maths

    Tonio
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