A9_2011 - University of Toronto at Scarborough Department...

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University of Toronto at Scarborough MAT A37H Summer 2011 Assignment # 9 You are expected to work on this assignment prior to your tutorial during the week of July 18th. You may ask questions about this assignment in that tutorial. At the beginning of your TUTORIAL during the week of July 25th you need to submit the following homework problems. STUDY: Chapter 11, Chapter 13. HOMEWORK PROBLEMS: 1. Let n N be arbitrary. Use MVT to prove Bernoulli’s inequality for x > 0: (1 + x ) n 1 + nx . 2. Does such a function exist? f is continuous and differentiable for all x R , and f (0) = - 1 , f (2) = 4, and f 0 ( x ) 2 for all x R . 3. Spivak #13.20(a)(b)(c) 4. Let f ( x ) = 0 , if 0 x 1 2 1 , if 1 2 < x 1 1 . 5 , if 1 < x 2 Show that R 2 0 f exists by applying the integrability reformulation (Theorem 2 of Chap- ter 13). EXERCISES:
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A9_2011 - University of Toronto at Scarborough Department...

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