MAT 302 ANALYSIS II CA 2023

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MAT 302: Test II for MAT302 Analysis II, Department of Mathematics, Faculty of Science, University of Buea, 23 May 2023. Exercise 1: definitions of continuity, uniform continuity, pointwise/uniform convergence, fixed points and contraction maps, plus statements of the Uniform Cauchy Criterion, Weierstrass M-Test and Contraction Mapping Principle. Exercise 2: Lipschitz implies uniformly continuous, and the non-expansive map f(x)=sqrt(x^2+1) on R having no fixed point without contradicting the Contraction Mapping Principle. Exercise 3: uniform convergence of an alternating series via the Alternating Series Test's uniform remainder bound, and pointwise (but not uniform) convergence of f_n(x)=x/n on R.