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 aset. All you are saying here is that 2.62 islessthan 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"?