Question: (b) Give an example of a function f : [0,1] > R that is not bounded. [3] (c) Let f : [1,1] > R be

(b) Give an example of a function f : [0,1] > R that is not bounded. [3] (c) Let f : [1,1] > R be a continuous function. Prove that the sequence (33\") defined inductively by 1 xn 36"\" = 3071+ 27f(1+ Ixnl )7 Cl31:07 converges. You may use theorems from the lecture as long as you state them explicitly. [8]

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