I have the following doubts. Please help me get through them..... (1) Is there any difference between the terms 'limit does not exist' and 'limit is not defined'? (2) For a limit to exist does it have to be a finite number? (3) When we do the algebra of limits as lim (x->a) [f(x) + g(x)] = [lim (x->a) f(x)] + [lim (x->a) g(x)], is it the necessary condition for both the limits to be finite? (4) When can we write 1/x as 0, as x->0. (This part is very confusing. Some insight or examples would be great.) (5)What is the basis of the L'Hospital's Rule??? (6) Are there any 'if s' to the Taylor series. If Yes, what are they???