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Assignment5(1804)(v2-6-4-11)

# Assignment5(1804)(v2-6-4-11) - A5/MATH1804/2010-11/2nd THE...

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A5/MATH1804/2010-11/2nd THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1804 University Mathematics A Assignment 5 Due date : Apr 14, 2011 before 17:00. Remember to write down your Name , Uni. number and Tutorial Group number . You are welcome to see the instructor or the demonstrators if you have any difficulties. See “Course information” at http://hkumath.hku.hk/course/MATH1804 for availabilities. Please drop your work in the assignment box marked MATH1804 on the 4th floor of Run Run Shaw Building. No late work will be accepted. 1. (L’Hˆ opital’s rule + Fundamental Theorem of Calculus) Compute lim x 0 Z x 0 t sin(sin t ) dt x 3 . (See also [December 2009 Exam, Problem 6].) 2. (Integration by substitution) Evaluate the following integrals using suitable substitutions. (a) Z dx (1 + x ) 2 x (b) Z cos(ln x ) x dx (c) Z s ds (1 - s 4 ) (You may need a formula which can be found in the worksheet of Tutorial 3.) 3. (Integration by parts) Evaluate the following integrals using integration by parts.

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Assignment5(1804)(v2-6-4-11) - A5/MATH1804/2010-11/2nd THE...

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