final_01_Spring

# final_01_Spring - Math 100 - Introduction to Multivariable...

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Unformatted text preview: Math 100 - Introduction to Multivariable Calculus FINAL EXAMINATION Spring Semester, 2001 Time Allowed: 2 Hours. Total Marks: 100 Student Name: Student Number: 1. (20 marks) Show that for any continuous function f ( x,y ), Z a Z x f ( x,y ) dy ¶ dx = Z a Z a y f ( x,y ) dx ¶ dy. 2. (15 marks) Find the angle α , which is formed by the x-axis and the ray as in the following figure, such that the two shaded regions have the same area. Here the two circles are C 1 : x 2 + y 2 = 4 and C 2 : x 2 + ( y- 1) 2 = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . ........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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## This note was uploaded on 09/30/2010 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

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final_01_Spring - Math 100 - Introduction to Multivariable...

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