MAT 302 Analysis II CA 2026

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MAT 302: Test II, University of Buea, Faculty of Science, Department of Mathematics, Course MAT302 Analysis II, 12/06/2026. Exercise 1 (12 marks): definitions of continuity, uniform continuity, pointwise/uniform convergence, fixed point, contraction map, and statements of the Uniform Cauchy Criterion, Weierstrass M-Test and Contraction Mapping Principle. Exercise 2 (10 marks): proving Lipschitz implies uniformly continuous, and analysing f(x)=ln(e^x+1) for the Lipschitz bound, absence of a fixed point, and why this does not contradict the Contraction Mapping Principle. Exercise 3 (10 marks): uniform convergence of a series via the Weierstrass M-Test, and pointwise vs uniform convergence analysis of f_n(x)=nx/(1+nx) on [0,infinity) and on [a,infinity).