Assignment:
Prove that:
- If lim f(x) as x->c exists but has a value different from f(c) the discontinuity at c is called removable,
- If lim f(x) as x->c^+ not =lim f(x) as x->c^-, then f has a jump discontinuity at c,
- If lim f(x) as x->c does not exists for some other reason the discontinuity at c is called essential discontinuity.
Provide complete and step by step solution for the question and show calculations and use formulas.