How do I prove the 3 types of discontinuity?
(Point/Removable, Jump, Infinite)

Question

How do I prove the 3 types of discontinuity? 
(Point/Removable, Jump, Infinite)

anonymous · Answer

Find the discontinuities, where f(x) is not defined. Point and removable discontinuities are where the limits converge to a number. Jumps are where they converge to two different numbers from two sides. Infinite discontinuitites are where they diverge.

anonymous · Answer

Thanks, but how would I explain/show that algebraically?

kainui · Answer

Compare the left hand and right hand limits. If they are not equal, then you have a jump discontinuity. If they are equal, and the limit exists, but the function at that point does not exist, then you have a removable discontinuity. An infinite discontinuity occurs when the limit at that point is equal to positive or negative infinity. I hope that explains how, any more clarification I'd be happy to help!