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Pre-Calc Homework Solutions 347

Pre-Calc Homework Solutions 347 - Section 8.4 11 t 3 t3 347...

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11. t 3 1 t 2 2 2 t 5 t ( t 2 1 t 2 2) 5 t ( t 1 2)( t 2 1) } t 3 1 t 1 2 2 2 t } 5 } A t } 1 } t 1 B 2 } 1 } t 2 C 1 } 1 5 A ( t 1 2)( t 2 1) 1 B ( t )( t 2 1) 1 C ( t )( t 1 2) 5 A ( t 2 1 t 2 2) 1 B ( t 2 2 t ) 1 C ( t 2 1 2 t ) 5 ( A 1 B 1 C ) t 2 1 ( A 2 B 1 2 C ) t 2 2 A Equating coefficients of like terms gives A 1 B 1 C 5 0, A 2 B 1 2 C 5 0, and 2 2 A 5 1. Solving the system simultaneously yields A 5 2 } 1 2 } , B 5 } 1 6 } , C 5 } 1 3 } . E } t 3 1 d t 2 t 2 2 t } 5 E } 2 1 t /2 } dt 1 E } t 1 1 /6 2 } dt 1 E } t 1 2 /3 1 } dt 5 2 } 1 2 } ln ) t ) 1 } 1 6 } ln ) t 1 2 ) 1 } 1 3 } ln ) t 2 1 ) 1 C 12. 2 t 3 2 8 t 5 2 t ( t 2 2 4) 5 2 t ( t 2 2)( t 1 2) } 2 t t 3 1 2 3 8 t } 5 } A t } 1 } t 2 B 2 } 1 } t 1 C 2 } t 1 3 5 2 A ( t 2 2)( t 1 2) 1 2 B ( t )( t 1 2) 1 2 C ( t )( t 2 2) 5 2 A ( t 2 2 4) 1 2 B ( t 2 1 2 t ) 1 2 C ( t 2 2 2 t ) 5 (2 A 1 2 B 1 2 C ) t 2 1 (4 B 2 4 C ) t 2 8 A Equating coefficients of like terms gives 2 A 1 2 B 1 2 C 5 0, 4 B 2 4 C 5 1, 2 8 A 5 3 Solving the system simultaneously yields A 5 2 } 3 8 } , B 5 } 1 5 6 } , C 5 } 1 1 6 } . E } 2 t t 3 1 2 3 8 t } dt 5 E } 2 3 t /8 } dt 1 E } t 5 2 /16 2 } dt 1 E } t 1 1 /16 2 } dt 5 2 } 3 8 } ln ) t ) 1 } 1 5 6 } ln ) t 2 2 ) 1 } 1 1 6 } ln ) t 1 2 ) 1 C 13.
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