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# HW 5 - Math E-21a Fall 2009 HW#5 problems Problems to turn...

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1 Math E-21a – Fall 2009 – HW #5 problems Problems to turn in on Thurs, Oct 8 : Section 11.2 : In problems 10 and 11, find the limit, if it exists, or show that the limit does not exist. 10. 3 4 4 ( , ) (0,0) 6 lim 2 x y x y x y 11. 2 2 ( , ) (0,0) lim x y xy x y Section 11.3 : 37. Find the indicated partial derivative: ( , , ) ; (3,2,1) z x f x y z f y z 68. Show that the Cobb-Douglas production function ( , ) P L K bL K satisfies the equation ( ) P P L K P L K Section 11.4 : 4. Find an equation of the tangent plane to the given surface at the specified point: ln , (1,4,0) z y x 28. Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and 4 cm in diameter if the metal in the top and bottom is 0.1 cm thick and the metal in the sides is 0.05 cm thick. 31. If R is the total resistance of three resistors, connected in parallel, with resistances R 1 , R 2 , and R 3 , then 1 2 3 1 1 1 1 R R R R If the resistances are measured in ohms as R 1 = 25 , R 2 = 40 , and R 3 = 50 , with a possible error of 0.5% in each case, estimate the maximum error in the calculated value of R . 38. Suppose you need to know an equation of the tangent plane to a surface S at the point P (2,1,3). You don’t have an equation for S but you know that the curves 2 2 1 ( ) 2 3 ,1 ,3 4 t t t t t

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