I need help understanding these problems

A. There is a theorem that says: Suppose that lim f (x) = L then, lim f (n) = L Where f(x) is a function whose domain is a set of real numbers and f(n) is a series whose domain is the set of positive integers, and if x = n then f(x) = f(n). If lim f(n) = L then lim f (x) = L may not be true. For example: lim cos(27n) = 1 for all n, yet lim cos(2x x) = undefined. Explain what is happening. B. In the Ratio Test, if lim an+1 > 1, which is bigger (d,.. | or |a,, | ? Explain why an this requires the series _ a,, diverges. 1=1 C. Explain why the Taylor Series with center c = 0, of f(x) = x2 - 1 is simply X2 - 1