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Unformatted text preview: Math 31BH  Homework 2. Due January 25. Part I. 1. ( Wednesday, Jan 12. ) Using the δ definition, show that the sequence x n = n 2 n 2 + 1 , 1 √ n converges and find its limit. 2. ( Friday, Jan 14. ) For the two functions (a) f ( x,y ) = 2 x 2 y (b) f ( x,y ) = 2 ( x 1) 2 y 2 answer the following questions: (i) draw the graph in 3space (ii) sketch the level curves (iii) sketch the cross sections 3. ( Wednesday, Jan 19. ) From the textbook solve the following problems: 1 . 7 . 2 , 1 . 7 . 4( a ) , 1 . 7 . 5 , 1 . 7 . 6 . 4. ( Friday, Jan 21. ) In each of the following, differentiate the function f in the direction of the vector at the given point: (a) f ( x,y ) = x 3 + 2 y 3 , at (1 , 1) in the direction i j √ 2 . (b) f ( x,y ) = x sin y + y cos x at (0 ,π/ 2) in the direction 3 5 i + 4 5 j . 5. ( Friday, Jan 21. ) Consider the function f ( x,y ) = y x 2 . (i) Draw the level curves of this function; (ii) using your knowledge of one variable calculus, find the tangent at P...
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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.
 Winter '11
 DragosOprea
 Math

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