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21c_02f_2be

# 21c_02f_2be - ∂ 2 g ∂s ∂t and ∂ 2 g ∂t ∂s in...

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Bender Math 21C Second Midterm Nov. 25, 2002 PRINT NAME Write version on your blue book and VERSION B hand in this exam inside your blue book. Put your name, ID number, and section number (or time) on your blue book. You may have ONE PAGE of notes. NO CALCULATORS are allowed. You must show your work to receive credit. 1. (24 pts.) Suppose g ( x, y ) is “well behaved” (that is, you can differentiate it as much as you want and those derivatives are continuous), x = 2 s + t and y = s - t . (a) Express ∂g ∂s in terms of g x and g y ONLY. “ONLY” means that neither s nor t should appear in your answer. (b) Express
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Unformatted text preview: ∂ 2 g ∂s ∂t and ∂ 2 g ∂t ∂s in terms of g xx , g xy and g yy ONLY. For problems 2, 3, and 4 f ( x, y ) = x 2 + y 3 + y 2 + 4 xy . 2. (36 pts.) (a) For what value of u is D u f (0 , 1) a maximum? (b) What is the maximum value of D u f (0 , 1)? (c) Find a value of u so that D u f (0 , 1) = 0. 3. (12 pts) Find the tangent line to the level curve f ( x, y ) = 2 at (0 , 1). 4. (28 pts) (a) Find the critical points of f ( x, y ). (b) Use the second derivative test to classify them. END OF EXAM Final Exam: 11:30 Wed. 12/11 in YORK 2722...
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