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Pre-Calc Homework Solutions 378

# Pre-Calc Homework Solutions 378 - 378 Section 9.3 Alternate...

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12. continued Alternate method: Using graphing techniques, we find that when ) x ) , 0.5, ) error ) 5 ) cos x 2 1 1 2 } x 2 2 } 2 ) , ) cos 0.5 2 1 1 2 } 0. 2 5 2 } 2 ) < 0.002583. The quantity 1 2 } x 2 2 } tends to be too small, as shown by the graphs of y 5 cos x and y 5 1 2 } x 2 2 } . [ 2 p , p ] by [ 2 1.5, 1.5] 13. Let f ( x ) 5 sin x . Then P 2 ( x ) 5 P 1 ( x ) 5 x , so we may use the Remainder Estimation Theorem with n 5 2. Since ) f - ( x ) ) 5 ) 2 cos x ) # 1 for all x , we may use M 5 r 5 1, giving ) R 2 ( x ) ) # } ) 3 x ) ! 3 } . Thus, for ) x ) , 10 2 3 , the maximum possible error is about } (10 3 2 ! 3 ) 3 } < 1.67 3 10 2 10 . Alternate method: Using graphing techniques, we find that when ) x ) , 10 2 3 , ) error ) 5 ) sin x 2 x ) # ) sin 10 2 3 2 10 2 3 )< 1.67 3 10 2 10 . The inequality x , sin x is true for x , 0, as we may see by graphing y 5 sin x 2 x . [ 2 10 2 3 ,10 2 3 ] by [ 2 2 3 10 2 10 ,2 3 10 2 10 ] 14. Let f ( x ) 5 ˇ 1 w 1 w x w . Then P 1 ( x ) 5 1 1 }
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