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? asked in Science & MathematicsMathematics · 4 years ago

Question with essential discontinuities?

so for

i) y = 1 and is undefined at y = 3

ii) y = 2 and is undefined at y = -1

iii)y = 1

I don't understand questions iv) and v), can someone help me out ? thank you

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1 Answer

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  • anonymous
    Lv 7
    4 years ago

    A function f(x) has an essential discontinuity at x = a if either of these are true:

    i) the sides limits do not coincide

    ii) one or both of the side limits are infinite

    For part iv, the discontinuity at x = 2 is an essential discontinuity because the side limits do not coincide. The discontinuity at x = 4 is an essential discontinuity because the limit as x approaches 4 from the right does not exist, i.e., f(x) goes to negative infinity as x approaches 4 from the right..

    For part v, the discontinuity at x = 0 is removable. You can remove the discontinuity at x = 0 by changing the piecewise definition to f(x) = 3 when x = 0.

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