1. (a) Consider the set S {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and Max(S). nex}. 2n :ne N 1 3n +1 (b) Let B = 1 i. Prove that inf B 2 ii. Show sup B = 3 (c) If r, y ER such that r> 0 and y> 0. Using the fact that,rE R, a2 2 0, prove each of the following. 1 xyS(x+y). i. Vry 2 1 ii. ry <; (x² + y*).

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.