need help with three conceptual calculus problems!
ok so 1.
true or false (and provide reasoning, not a full length proof) that
lim as x -> a of f(x)*g(x) can not exist
if lim x->a f(x) and lim x->a g(x) both exist
so its kind of a reasoning to show that the product limit law always works if both limits exist?
2. In the formal definition of limits: lim x->c f(x) = L, if for every E>0 there is a d>0 such that IF 0<|x-c|<d THEN |f(x)-L|<E
can you switch the inequalities after the IF and THEN, and does the definition still hold?
3. TRUE or FALSE
f(x) = 1 if x is rational
= 2 if x is irrational
the limit as X-->0 exists for f(x)
im not sure about this one cause of whether the right and left hand limits meet and if so, at 1 or 2??!?!
thanks! please do asap