Please help me with this question, thank you.

Let X, Y be metric spaces. Recall the following definitions: For f : X - R, lim f(x) = lim sup { f(x) | x E Bs(a)} 6-0 lim f(x) = lim inf { f(x) | x E Bs(a)} 6-0 For f : X - Y we say that lim.-a f(x) = y V= > 0 38 > 0 such that f(Bs(a)) C BE(f (a)). (a) For real valued f prove that lime->a f(x) =y limx->a f(x) =lim> >a f(x) = y. (b) Prove that lime-a f(x) = y for every sequence In -+ a we have f(In) - y. (c) Let f : R - R. How do you have to modify the above definitions and statements if x approches a from the right, i.e. we look at right-hand limits x - at