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| dD maro2.matnmcail.ca: H263 WINTER20186,5/?effectiweUser 250725640Buser 260 WeBWorK d, MAA MATHEMATICAL ASSOCIATION OF AMERICA Logged in as 260725640 Log Out webwork math263 winter2018 65 MAIN MENU Courses Homework Sets 6: Problem 5 Problem 5 User Settings Previous Problem List Next Grades (1 point) Determine the first three nonzero terms of the Taylor polynomial approximations for the given initial value problem. y'- 7siny + 2er, y(0)-0 Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Preview My AnswersSubmit Answers You have attempted this problem 0 times. You have unlimited attempts remaining Email instructor Page generated a 03/25 2018 at 05.46pm EDT weBworK© 1996-2016 l theme; math4 1 ww version: 2.11 l pg version: 2.111 The weBworK ProjectExplanation / Answer
y' = 7siny + 2ex
y(0) = 0
y'(0) = 7 sin(y(0))+ 2e0
=> y'(0) = 0 + 2
=> y'(0) = 2
Now ,
y' = 7siny + 2ex
Differentiate wrt x
=> y'' = 7cosy . y' + 2ex
y''(0) = 7cos(y(0)).y'(0) + 2e0
=> y''(0) = 7* 2 + 2 = 14 + 2 = 16
y'' = 7cosy . y' + 2ex
Differentiate again wrt x
y''' = 7 ( cosy. y'' + y' -siny y ' ) + 2ex
y'''(0) = 7 ( 1 * 16 + 2*0)+ 2
=> y'''(0) = 7*16 + 2 = 112+2 = 114
Hence
y = y(0)+y(0)x+y(0) x2/2! + y'''(0)x3 / 3!+ ....
= 0 + 2x + 16x2/2 + 114x3 / 6+ .....
= 2x + 8x2 + 19x3 (Three non zero terms )
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