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Homework_8

# Homework_8 - Homework 8 Math 139 Due Oct 27th Instructor...

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Unformatted text preview: Homework 8 - Math 139 Due Oct 27th Instructor Oﬃce Oﬃce hours Web page Mauro Maggioni 293 Physics Bldg. Monday 1:30pm-3:30pm. www.math.duke.edu/˜ mauro/teaching.html Reading: from Reed’s textbook: Section 4.1,4.2 Problems: §3.3: #8, 13, 15 §4.1: #2,3,5,9,10,12 Additional Problem: Prove that if a function is continuous on the open interval (a, b) and bounded on [a, b] then it is Riemann integrable on [a, b]. (Hint: I already gave it in class: pick partitions with small intervals near the endpoints, and bound the diﬀerence between lower and upper Riemann sums at the endpoints separately from how you bound such diﬀerence on the internal intervals). Conclude that the function f , deﬁned on [0, 1] 1 by f (x) = sin x for x ∈ (0, 1] and f (0) = 7, is Riemann integrable on [0, 1]. ...
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