MATH 410 Study Guide - Final Guide: Bounded Function
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Math 410 spring 2016 boyle final exam. There are more questions on the other side. point (i. e. , a point x0 such that f (x0) = x0): (7 pts) suppose f : [a, b] [a, b] is continuous. Prove that f has a xed: (10 pts) (a) suppose f : [0, 1] r, with f (x) = x . Lipschitz. (b) suppose g : r r is di erentiable, with g bounded. Lipschitz: (5 pts) give an example of a bounded function f : (0, 1) r which is continuous but not uniformly continuous. No proof required: (8 pts) determine the radius of convergence of each of the following series. No proof required. (a: (7 pts) let = p7 assume 0 < e < 3. ) Prove that 0 < e < . 000 1. (you may. Prove p k=1 ak converges: (9 pts) compute the following limits. (possible answers: , , a num- ber or dne. ) lim n (cid:16)1 +