Bekki George Lecture notes 13

P6 x for f x sin x 2 b find

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Unformatted text preview: ! ! a) !Find! P6 ( x ) !for! f ( x) = sin( x 2 ) ! ! ! ! ! ! ! ! b) Find! P7 ( x ) !for! $ k !! f k (0) ! k! ! Example!4:! Use the values in the table below and the formula for Taylor polynomials to give the 4th degree Taylor polynomial for f centered at x = 0. f(0) f '(0) f ''(0) f '''(0) f (4) (0) -5 -2 -2 4 -5 ! ! ! ! ! ! ! ! ! ! ! Example!5:! Find the Taylor polynomial P4(x) for the given function. ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Taylor’s!Theorem:! If!f!has!n+1!continuous!derivatives!on!an!open!interval!that!contains!0,!then!for!each! f ' ' (0) 2 f n (0...
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