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].

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