# PS2_answers - xy = 0 except(0 0 B5 b One example f x,y = xy...

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Here are some answers to some of the problem set problems. I have, of course, not included ones in which the question asks to prove or verify something. Also, for now, I have not had a chance to include pictures. Math 237 Problem Set 2 Answers A4. Range - 1 z 1. | f ( x,y ) | ≤ 3 5 when ( x,y ) lies on our between y = 1 2 x 2 and y = 2 x 2 or between y = - 1 2 x 2 and y = - 2 x 2 . B1. i) continuous if f (0 , 0) = 0. ii) continuous if f (0 , 0) = 0. iii) limit does not exist (try lines y = mx 1 / 3 ) iv) limits does not exist (try lines x = 0, y = 0) v) continuous if f (0 , 0) = 0. vi) limit does not exist (try lines x = 0, y = 0) vii) continuous if f (0 , 0) = - 2 B2. a) lim ( x,y ) (0 , 0) f ( x,y ) = 2. b) f (0 , 0) = 2. B4. a) f x (1 , - 4) = 1, f x (0 , 0) = 0, f x (0 , 1) does not exist. b) The partial derivatives of f do not exist at all points where
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Unformatted text preview: xy = 0, except (0 , 0). B5. b) One example f ( x,y ) = xy x 2 + y 2 B7. i) a) diﬀerentiable, b) continuous, c) no info ii) a) not diﬀerentiable, b) no info, c) at least one partial not continuous iii) a) diﬀerentiable, b) continous, c) no info. iv) a) not diﬀerentiable, b) no info, c) at least one partial not continuous B8. i) does not exist ii) does not exist iii) does not exist iv) exists and equals 0 B9. a) One example f ( x,y ) = p | ( x-1)( y-2) | b) One example f ( x,y ) = p | 1-x 2-y 2 | B10. f ( x,y ) = | x | . B11. b) The limit exists and equals 0. 1...
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