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    Removable discontinuity, jump and essential discontinuities.

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    Prove that
    a- if lim f(x) as x->c exists but has a value different from f(c) the discontinuity at c is called removable,
    b-if lim f(x) as x->c^+ not =lim f(x) as x->c^-, then f has a jump discontinuity at c,
    c-if lim f(x) as x->c does not exists for some other reason the discontinuity at c is called essential discontinuity.

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    https://brainmass.com/math/real-analysis/removable-discontinuity-jump-and-essential-discontinuities-29769

    Solution Summary

    This solution is comprised of a detailed explanation for removable discontinuity, jump discontinuity and essential discontinuity.
    It contains step-by-step explanation for the following problem:
    Prove that
    a- if lim f(x) as x->c exists but has a value different from f(c) the discontinuity at c is called removable,
    b-if lim f(x) as x->c^+ not =lim f(x) as x->c^-, then f has a jump discontinuity at c,
    c-if lim f(x) as x->c does not exists for some other reason the discontinuity at c is called essential discontinuity.

    Solution contains detailed step-by-step explanation.

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