Let f: (0, 1]→R be given by f(z) = { cos() for z>0 for z = 0 (a) For 0< 6 < 1 let fs denote the restriction of f to the interval (6, 1]. Explain why fSs is Riemann integrable. (b) Find suitable extensions a and w of fs to the interval (0, 1] that satisfy the hypotheses of the Squeeze Theorem. (c) Verify that your a and w satisfy the hypotheses and conclude that f is Riemann integrable on the interval (0, 1].

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Let f: (0,1]→R be given by f(2) ={ cost
cos(1) for r>0
for r = 0
(a) For 0 < 6 < 1 let fs denote the restriction of f to the interval (6, 1). Explain why fs
is Riemann integrable.
(b) Find suitable extensions a and w of fs to the interval (0, 1] that satisfy the hypotheses
of the Squeeze Theorem.
(c) Verify that your a and w satisfy the hypotheses and conclude that f is Riemann
integrable on the interval (0, 1].
Transcribed Image Text:2. Let f: (0,1]→R be given by f(2) ={ cost cos(1) for r>0 for r = 0 (a) For 0 < 6 < 1 let fs denote the restriction of f to the interval (6, 1). Explain why fs is Riemann integrable. (b) Find suitable extensions a and w of fs to the interval (0, 1] that satisfy the hypotheses of the Squeeze Theorem. (c) Verify that your a and w satisfy the hypotheses and conclude that f is Riemann integrable on the interval (0, 1].
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