m222-pract

m222-pract - Sample of problems (1) Interchanging the...

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Unformatted text preview: Sample of problems (1) Interchanging the orders of integration for the double integral R π 2 R cos x y sin x dydx gives: (a) R sin x y dy R cos y sin x dx , (b) R cos y sin x dx R 1 y dy , (c) R π 2 y =0 R cos- 1 x y sin x dxdy , (d) R 1 R cos- 1 y y sin x dx dy , (e) R 1 R cos y y sin x dxdy . Answer: (d) (2) Let x ( y,z ) be defined implicitly by xy 3 = 2 y- z . Then ∂x ∂y ¶ 2 + ∂x ∂z ¶ 2 at the point (0 , 1 , 2) has the value (a)- . 2, (b) 0 . 2, (c) 5, (d) 2, (e)- . 5. Answer: (c) (3) Define z = Z ( x,y ) implicitly by x 2 + xy + yz + z 2 = 3 with Z (1 , 2) = 0. The directional derivative at (1 , 2) in the direction of the vector (3 ,- 4) is (a)- . 8, (b)- 8, (c)- 2 . 8, (d) 2 . 8, (e) 0 . 8. Answer: (a) (4) Of the two infinite series A : ∞ X n =1 (- 1) n e- n 2 ln( n + 1) , B : ∞ X n =1 √ n 2 + 4 n 2 (a) both are absolutely convergent (b) both are divergent (c) A is divergent and B is convergent (d) A is absolutely convergent and B is divergent (e) A is absolutely convergent and...
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This note was uploaded on 05/01/2008 for the course MATH 222 taught by Professor Karlpeterrussell during the Winter '08 term at McGill.

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m222-pract - Sample of problems (1) Interchanging the...

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