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Unformatted text preview: Homework 8 - Math 139
Due Oct 27th Instructor
Web page Mauro Maggioni
293 Physics Bldg.
www.math.duke.edu/˜ mauro/teaching.html Reading: from Reed’s textbook: Section 4.1,4.2
§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]
by f (x) = sin x for x ∈ (0, 1] and f (0) = 7, is Riemann integrable on [0, 1]. ...
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This note was uploaded on 01/16/2012 for the course MATH 139 taught by Professor Pardon,w during the Fall '08 term at Duke.
- Fall '08