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Unformatted text preview: for all . (You may use for each . Solution Since , . Hence, we have where and c is some point between 0 and x . Since , we have for each . It follows that (10 Marks)The power series representation for the function begins Find the coefficient of in the series. Solution Since for , the coefficient of is (20 Marks)A function f ( x ) satisfies f (1)=3, and its first four derivatives are as follows: Unfortunately, we do not know a formula for f ( x ). ( i ) Find , the Taylor polynomial of order 3 based at a =1. ( ii ) Give a bound for , the error in Taylor's Formula with n =3. Solution ( i ) f (1)=3, , and . Hence, we have ( ii ) Since , Hence, when 1< c <1.5, we have Since , we have (20 Marks)Use a calculator to estimate using the Trapezoidal Rule with n =3 (Three decimal places are enough). Solution , a =2, b =4 and n =3. Then we have h =( ba )/ n =(42)/3=2/3. , , , , • About this document . .. Next: About this document Kunquan Lan Tue Mar 7 16:47:02 EST 2000...
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 Fall '09
 ganong
 Math, Taylor Series, Mathematical Series, 1014.03MW

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