A9_2011 - University of Toronto at Scarborough Department...

This preview shows pages 1–2. Sign up to view the full content.

University of Toronto at Scarborough Department of Computer & Mathematical Sciences 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: You do not need to submit these questions but you should make sure that you are able to answer them; 1. Spivak # 11.30(a)(b), 11.37(a)(b), 11.41(a)(b), 11.51, 11.52, 11.53, 11.64, 13.1, 13.2, 13.7(i)(iii)(v)(vii), 13.11(a)-(c), 13.12, 13.13, 13.15, 13.33(a), 13.37

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. Show that the equation
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern