hwk5 - Math 31BH - Homework 5. Due Tuesday, February 15. 1....

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Math 31BH - Homework 5. Due Tuesday, February 15. 1. ( Wednesday, February 9. ) Pathological functions. From the textbook, solve 1 . 9 . 1 and 1 . 9 . 2 . 2. ( Wednesday, February 9. ) Pathological functions and second order derivatives. Put f ( x,y ) = ( xy · x 2 - y 2 x 2 + y 2 if ( x,y ) 6 = (0 , 0) 0 if ( x,y ) = (0 , 0) . (i) Calculate the ﬁrst derivative f x at (0 , 0) directly from the deﬁnition. (ii) Calculate the ﬁrst derivative f x at any other point ( x,y ) 6 = (0 , 0) . (iii) Differentiate once more i.e. calculate f xy (0 , 0) using the deﬁnition. Conﬁrm that f xy (0 , 0) = 1 . (iv) Repeat for the derivative f y (0 , 0) then f yx (0 , 0) . Conﬁrm that f yx (0 , 0) = - 1 . Observe that f xy (0 , 0) 6 = f yx (0 , 0) . 3. ( Monday, February 14. ) From the textbook solve 3 . 6 . 1 , 3 . 6 . 2 , 3 . 6 . 7 . 4. ( Monday, February 14. ) Two space shuttles are at the points (1 , 0 , - 1) and (6 , 1 , 0) at time 0 and are travelling in straight lines parallel to the vectors - 2 i + j and 4 i - j - k . What is the
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This note was uploaded on 03/28/2011 for the course MATH 31B taught by Professor Dragosoprea during the Winter '11 term at UCSD.

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