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Homework Assignment

# Homework Assignment - Homework 6 There are so many good...

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Homework 1: TBB exercises: 2.8.2, 2.9.2, 2.11.3, 2.11.6, 2.12.3, 5.1.16 Homework 2: TBB exercises: 5.4.8, 5.5.1, 5.5.2, 5.6.3, 5.6.9 Show that the image of a compact set under a continuous function is compact. Homework 3: TBB exercises: 7.2.2,7.2.3,7.2.11,7.2.15 Show that the function sin(1/x) is not differentiable at x=0. Is sin(1/x) uniformly continuous on the interval (0,1)? Show that the function sin(x)/x is uniformly continuous on (0,1). You may use l'Hoptial's rule to compute limits and assume sin(x) is continuous on the real line. Homework 4: TBB exercises: 7.3.3, 7.3.18, 7.6.2, 7.6.6, 7.6.13 Homework 5: TBB exercises: 7.11.3,7.11.5, 7.12.5, 7.12.6 TBB exercises: 3.4.3, 3.4.14
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Unformatted text preview: Homework 6: There are so many good problems on series in the text, I had trouble setting this week's assignment! We'll have lot's of good problems on series convergence tests on next week's homework. TBB exercises: 3.4.15, 3.4.16, 3.4.26, 3.4.27, 3.5.1, 3.6.6 Homework 7: Note: for exercise 3.6.2 parts c,e, and f discuss the different behaviors for different values of the constants s and t. Hint for 3.6.23: show that the sum is an approximation of an integral. TBB exercises: 3.6.2, 3.6.3 parts a-c, 3.6.7, 3.6.20, 3.6.23 Homework 8: TBB problems on power series: 10.2.8, 10.2.12 TBB problems on metric spaces: 13.2.4, 13.4.7, 13.6.1, 11.7.12,...
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