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assignment2 - MATH1211/10-11(2)/A2/NKT THE UNIVERSITY OF...

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Unformatted text preview: MATH1211/10-11(2)/A2/NKT THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 2nd Semester: Assignment 2 Due date: 2011 February 9 (Wednesday), 5:00pm. (The Exercise/problem numbers in the following refer to those in the textbook.) 1. Evaluate the limits in the following, or explain why the limit fails to exist. (a) lim ( x,y ) → (0 , 0) 2 xy x 2 + y 2 (b) lim ( x,y,z ) → (0 , , 0) y 3- 1000 xy 2 + z 5 x 2 + y 2 + z 4 2. ( § 2.2 no.23) Examine the behavior of f ( x,y ) = x 4 y 4 / ( x 2 + y 4 ) 3 as ( x,y ) approaches (0 , 0) along various straight lines. From your observations, what might you conjecture lim ( x,y ) → (0 , 0) f ( x,y ) to be? Next consider what happens when ( x,y ) approaches (0 , 0) along the curve x = y 2 . Does lim ( x,y ) → (0 , 0) f ( x,y ) exist? Why or why not? 3. Determine, with explanation, whether the following functions are continuous throughout their domains: (a) ( § 2.2 no.40) g ( x,y ) = ( x 3 + x 2 + xy 2...
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This note was uploaded on 05/04/2011 for the course MATH 1211 taught by Professor Wang during the Spring '11 term at HKU.

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assignment2 - MATH1211/10-11(2)/A2/NKT THE UNIVERSITY OF...

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