Criteria for Success: I can . use Calculus 1 techniques such as L'Hospital's Rule and Squeeze Theorem to find limits of sequences . determine convergence or divergence of a sequence numerically and graphically . given a bound ( E > 0) for the difference between the terms of a convergent sequence and its limit, determine the minimal index that achieves that bound Question: Consider the sequence given by an = )"An for n 2 1. 2n - 1 (a) Look at its graph and the numerical pattern of its terms to determine its limit as n tends to co or conclude that it does not exist. Listing terms and/or a sketch of a graph here are appropriate justifications. (b) Confirm your observation by using Calculus 1 limit properties and theorems. Note that heuris- tic arguments derived by looking at the degrees of the numerator and denominator, while very valuable for intuition, are not good enough justification here. Hint: Consider the limits when n values are even or odd seperately. (c) If the answer to part (b) above is that the limit does not exist, or is too, then you don't need to answer this part. Otherwise, let L be the limit you found above, and find the minimal index N so that for n 2 N, we have lan - LI