152sum2003MT2_2 - Let f x,y be defined as f x,y = sin x 3...

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Last Name Name Student No Department Section Signature : : : : : : : : : : : : : Code Acad. Year Semester Instructors Date Time Duration M E T U Department of Mathematics Calculus-II II. Midterm Math 152 2004 Summer A. ¨ O., M.K., B.K. 30.07.2004 19.00 90 minutes 4 Questions on 4 Pages Total 60 Points 1 2 3 4 Question 1 (12+6 pts.) (a) Find an equation of the plane passing through the points A = (0 , 0 , 0), B = (1 , 2 , 3) and C = ( - 1 , - 2 , 3). (b) Is the point (3 , 2 , 1) on the plane you found in part (a) ? Explain.
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Question 2 (5+5+5 pts.) Evaluate the following limits if they exist. (a) lim ( x,y ) (0 , 0) yx 3 x 2 + y 4 (b) lim ( x,y ) (0 , 0) x 3 y x 6 + y 2 (c) lim ( x,y ) (1 , 0) xy x 2 + y 2
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Question 3 (12 pts.)
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Unformatted text preview: Let f ( x,y ) be defined as f ( x,y ) = sin( x 3 + y ) x 2 + y 2 , ( x,y ) 6 = (0 , 0) , ( x,y ) = (0 , 0) . Find ∂f ∂x (0 , 0) and ∂f ∂y (0 , 0) if they exist. Question 4 (10+5 pts.) Let z = f ( x,y ) = g ( x 2 y, x-y, x 2 + y ). (a) Find ∂f ∂x and ∂f ∂y at ( x,y ) = (1 , 1), if g 1 (1 , , 2) =-2, g 2 (1 , , 2) = 3 and g 3 (1 , , 2) = 1. (b) Find the normal line to the graph of f ( x,y ) at (1 , 1), if g (1 , , 2) = 5 ....
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152sum2003MT2_2 - Let f x,y be defined as f x,y = sin x 3...

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