quiz4sol - November 8 2011 Name Name.nnn TA& Rec hour...

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Unformatted text preview: November 8, 2011 Name Name.nnn TA & Rec. hour Math. 152 – Quiz 4 – Form A PROBLEM 1. (10 points) Write down the general form of the partial fractions decomposition of ( x- 17) 9 ( x 4 + 16 x 2 )( x 2- 11 x + 30) 2 Do NOT determine the numerical values of the coefficients. Solution. Since deg[( x- 17) 9 ] = 9 and deg[( x 4 + 16 x 2 )( x 2- 11 x + 30) 2 )] = 8, it follows that ( x- 17) 9 ( x 4 + 16 x 2 )( x 2- 11 x + 30) 2 = Ax + B + R ( x ) ( x 4 + 16 x 2 )( x 2- 11 x + 30) 2 , where A and B are real constants and R ( x ) is a polynomial and deg[ R ( x )] < 8. Since x 4 + 16 x 2 = x 2 ( x 2 + 16) and x 2- 11 x + 30 = ( x- 5)( x- 6) , it follows that the partial fraction decomposition of ( x- 17) 9 ( x 4 +16 x 2 )( x 2- 11 x +30) 2 has the form Ax 1 + B 1 + C x 1 + D x 2 1 + Ex + F x 2 + 16 2 + G x- 5 1 + H ( x- 5) 2 1 + I x- 6 1 + J ( x- 6) 2 1 , where C , D , ··· , and J are constants....
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This note was uploaded on 11/11/2011 for the course MATH 152.01 taught by Professor Geline during the Fall '09 term at Ohio State.

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quiz4sol - November 8 2011 Name Name.nnn TA& Rec hour...

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