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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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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.

Solution provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
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