(b) Restricted Function: Let g be a bounded function on [0, 1] and assume that its restriction to the interval [1/n, 1] is Riemann integrable for every n > 2. You are to show that g is Riemann integrable on the entire interval [0, 1]. Hint: You're given to let € > 0 and M > 0 be constants such that g(x)| ≤ M for all z in [0, 1]. Choose n > 2 such that <3 and note that the supremum and infimum of g on [0,1/n] differ by less than ². 3M You are to show that g is Riemann integrable on [1/n, 1] and find an appropriate partition of [0, 1].
(b) Restricted Function: Let g be a bounded function on [0, 1] and assume that its restriction to the interval [1/n, 1] is Riemann integrable for every n > 2. You are to show that g is Riemann integrable on the entire interval [0, 1]. Hint: You're given to let € > 0 and M > 0 be constants such that g(x)| ≤ M for all z in [0, 1]. Choose n > 2 such that <3 and note that the supremum and infimum of g on [0,1/n] differ by less than ². 3M You are to show that g is Riemann integrable on [1/n, 1] and find an appropriate partition of [0, 1].
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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![(b) Restricted Function: Let g be a bounded function on [0, 1] and assume that its restriction to the
interval [1/n, 1] is Riemann integrable for every n > 2. You are to show that g is Riemann
integrable on the entire interval [0, 1].
Hint: You're given to let € > 0 and M > 0 be constants such that g(x)| ≤ M for all z in [0, 1].
Choose n > 2 such that <3 and note that the supremum and infimum of g on [0,1/n] differ
by less than ².
3M
You are to show that g is Riemann integrable on [1/n, 1] and find an appropriate partition of [0, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f3f25b-2eb2-4186-b342-f9f487e8326d%2Faefa54d3-ad01-4b73-b686-45e7cbad3ae4%2Frk3xnfc_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Restricted Function: Let g be a bounded function on [0, 1] and assume that its restriction to the
interval [1/n, 1] is Riemann integrable for every n > 2. You are to show that g is Riemann
integrable on the entire interval [0, 1].
Hint: You're given to let € > 0 and M > 0 be constants such that g(x)| ≤ M for all z in [0, 1].
Choose n > 2 such that <3 and note that the supremum and infimum of g on [0,1/n] differ
by less than ².
3M
You are to show that g is Riemann integrable on [1/n, 1] and find an appropriate partition of [0, 1].
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