It's hard to understand what you are asking here. Is this problem exactly as you were given it? It seems strangely written. Why use absolute values signs for a specific positive number? |2.62| is just 2.62! And why say "upper bound" for a single number? An "upper bound" is for a set. All you are saying here is that 2.62 is less than the given numbers (which, as you say, is NOT true of 4). Since is a polynomial, it is continuous for all x and, in particular, for x= 2: the limit is so that "|f(x)- L|" is just . If x can be any number, and I see no restriction on it, there is no upper bound on that.
For the second question, we are given that "0< |x- 2|< 0.01", so that x lies between 1.99 and 2.01. The largest x can be is 2.01 so that largest that can be is . It looks to me like three of the given statements are true. What do you mean by "best"?