Sample Final Solutions

# Sample Final Solutions - 1 a dy 1 3 = 3 = 2 1 9x 1 9x 2 dx...

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( ) ( ) ( ) ( ) ( ) 1 2 2 2 2 2 2 2 2 1 1 2 1 sin 2 2 1 3 1. a. 3 1 9 1 9 6 ln 1 1 b. 3 ln 1 2 1 1 c. ln sin ln 1 1 1 ln sin 1 ln sin 1 1 2. 1 ln 1 1 2 x dy dx x x x x dy x x dx x x y x x dy x x y dx x x dy x x x dx x x dy x x y dy x dx y dx y = ⋅ = + + + = + = + + = = + = + = = = ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 ln 0 1 2 ln 1 2 2 2 1 1 1 3. a. Let 2 5 2 5 Using tabular integration by parts: 5 5 2 5 2 2 2 ln5 ln5 x x x u u u u C x C C y y e e y e e u x du dx x x dx u du u du u u + = + = − ⇒ = = = ± = = = = + ( ) ( ) ( ) 3 2 3 1 2 2 5 ln5 5 5 5 =2 4 2 ln5 ln5 ln5 1 3 b. sin 3 9 1 9 c. By integrati u x x x C x x C dx x dx C x x  +

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## This note was uploaded on 09/27/2009 for the course MATH 133 taught by Professor Wei during the Fall '07 term at Michigan State University.

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Sample Final Solutions - 1 a dy 1 3 = 3 = 2 1 9x 1 9x 2 dx...

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