MATH138 Final: MATH138, lec 4
15 Sep 2018
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Integration, review of taylor polys. , taylor series and. Q: say we know () and are avant a power series for it. Find in terms of ! and () = . Then () () = ( )( : if , then = min{,} (and the interval of con is the intersection of the 2 intervals), = , then (may be larges !) First, make the pacers on the same (). Next : () =1 + 22( ) + 33( )2 + . Keep going : () = 22 + 63( 4) + . Theorem : if () has a power series expansion about =, say () = . Closer look at theorem: no matter how you find a power series for , it is the taylor series. The order taylor paly for () = Ex: () = , ()(0) = 1, . So if has a power series representation, then = .
