10c_04f_2be

10c_04f_2be - , 1) = 3, g y (1 , 1) = 2, x (1) = 3, x (1) =...

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Math 10C Second Midterm 40 points November 17, 2004 Write version on your blue book VERSION B Put your name, ID number, and section number (or time) on your blue book. You may have ONE 2-sided page of notes. NO CALCULATORS are allowed. You must show your work to receive credit. 1. (12 points) The table at the bottom of this page gives wave heights ( w ) in feet produced by various wind speeds ( s in knots) blowing for various lengths of time ( t ) in hours. Thus we have a table of some values of w ( s, t ). (a) Estimate w (50 , 10) = a w s (50 , 10) , w t (50 , 10) A . (b) What are the units of each of these partial derivatives? (For example — but wrong — knots per hour.) (c) Estimate the wave height when a wind of 49 knots has been blowing for 11 hours. You can leave arithmetic like (27 / 4) × 3 1 in your answer. (Of course, this is not the answer.) 2. (12 points) Compute the indicated derivatives. (a) f (1) given that f ( t ) = g ( x ( t ) , y ( t )), g (3 , 1) = 4, g (1 , 1) = 3, g x (3 , 1) = 1, g y (3 , 1) = 2, g x (1
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Unformatted text preview: , 1) = 3, g y (1 , 1) = 2, x (1) = 3, x (1) = 1, y (1) = 2, and y (1) = 3. Misprint : y (1) = 2 should be y (1) = 1. (b) f y ( x, y ) x given that f ( x, y ) = x 3 y y cos 2 (ln y ). (c) D u f (0 , 1) given that f ( x, y ) = x 2 2 xy and u is a unit vector in the same direction as a 1 , 2 A . 3. (8 points) Find the equation of the tangent plane to the surface 3 x 2 + y 2 + 2 z 2 = 21 at the point (1 , 4 , 1). 4. (8 points) Find the local maxima, local minima and saddle points of the function f ( x, y ) = xy 2 x 2 y 2 +5. To help you with your calculations, the critical points are at (0 , 0), (1 , 2) and (1 , 2). Duration (hours) table of wave height (feet) 5 10 15 20 30 40 50 30 knots 9 13 16 17 18 19 19 40 knots 14 21 25 28 31 33 33 50 knots 19 29 36 40 45 48 50 60 knots 24 37 47 54 62 67 69 END OF EXAM...
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