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Unformatted text preview: dV z y x x x z y x > > + + + + , 1 2 / 5 2 2 2 2 3 2 2 2 ) ( converges. 8. Evaluate dA y x e R y x + + 2 2 2 ) ( ) ( 1 . HINT: Take squares as the sequence and apply suitable change of variables. } { j U 9. Evaluate dy y y 1 ln 1 . HINT: Define dy y y x F x = 1 ln 1 ) ( , x > 0. Evaluate (improper integral, modify and apply Th.4.47) and then integrate to get . ) ( x F ) ( x F 10. Verify that the improper integrals dx x 3 3 ) 1 ( 1 and dx x 1 1 2 1 diverge. Show that the first integral has a principal value and the second does not. HINT: set 2 1 = . Knowing: all the definitions, precise formulation of all the Theorems done on the lecture and the proofs of the few Theorems listed below is also part of the Assignment. 3.18, 4.46, 4.47, 4.65, 4.66 ....
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This note was uploaded on 10/21/2010 for the course MATHEMATIC MAT237Y1 taught by Professor Romauldstanczak during the Fall '09 term at University of Toronto Toronto.
 Fall '09
 RomauldStanczak
 Calculus, Parallelograms

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