MATH 242 Midterm: MATH242 Fall 2008 Exam
31 Jan 2019
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In questions 1-4 inclusive all proofs are to be given from rst principles. Only the most basic properties of real numbers may be assumed. Proofs must be self-contained and you must work directly from the de nitions of the concepts involved. This exam has 9 questions and 4 pages. 2 x2 for x 0 and n n. (ii) (1 point) (1 + x)2n+2 n4x4. 4 for x 0 and n n. (iii) (3 points) n34 n n . If f, g : r r and f (0) and g (0) exist and if h : r r is de ned by: (10 points) a continuous function f : [0, [ r satis es the inequality. |f (a + 1) f (b + 1)| |f (a) f (b)| for all a, b [0, [. Show that f is uniformly continuous on [0, [. Any theorem or theorems that you use in your proof should be carefully stated.
