# Removable discontinuity, jump and essential discontinuities.

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.

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.