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Unformatted text preview: ˆ opital’s rule11 University of Illinois Spring 2010 ECE 313: Problem Set 0 Calculus Review Due: Friday January 22 at 4 p.m. Reading: Ross Chapter 1.1–1.4, Chapter 2.1–2.5. Noncredit Exercises: Chap. 1: Probs. 15,7,9. Theoretical exercises 4,8,13. Selftest probs. 115. Chap. 2: Probs. 3,4,9,10, 1114. Theoretical exerecises 13,6,7,10,11,12,16,19,20. Selftest probs. 18. About the problems below: Calculus, a prerequisite of this course, will be used mainly in the second half of the semester. The parts of calculus primarily needed are integration and differentiation, Taylor series, L’Hˆ opital’s Rule, integration by parts, and double integrals (setting up limits of integration and change of variables such as in rectangular to polar coordinates). This problem set will help you review these topics, and identify areas in which you may need additional review. 1. [Geometric, MacLaurin, and Taylor series; L’Hˆopital’s rule] (a) Prove that 1 + x + x 2 + ··· + x n 1 = 1 − x n 1 − x for all x negationslash...
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 Spring '08
 Milenkovic,O
 Calculus, Derivative, Maclaurin Series, Taylor Series

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