MATH1211/10-11(2)/Tu2/TNK THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 2nd Semester: Tutorial 2 Date of tutorial classes: February 10–11. (The section/problem numbers in the following refer to those in the textbook.) 1. Find the matrix D f ( a ) of partial derivatives where f : R 2 → R 3 and a are given by f ( x,y ) = (2 x-y, y 3 , x sin xy ) , a = (1 ,-1) . 2. Let f : R 2 → R be the function deﬁned by f ( x,y ) = ( 1 if x = 0 or y = 0 ,0 if both x,y 6 = 0 . At each of the following points, (i) determine whether f is continuous, (ii) ﬁnd f x and f y (or show that they do not exist), and (iii) determine whether f is diﬀerentiable : (a) ( a,b ) where both a,b 6 = 0 (b) ( a, 0) where a 6 = 0 (c) (0 ,b ) where
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