Bekki George Lecture notes 13

# Forfatxais 2 3 f a f a f n a pn

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Unformatted text preview: mial!for!f!at!x\$=\$a\$is! ! 2 3 f ''( a ) f '''( a ) f n ( a) ! Pn ( x ) = f ( a ) + f '( a ) x − a + x−a + x − a ++ x−a ! 2! 3! n! !!provided!f!has!n!derivatives!at!a.! !! Example!!1:!!Find! P4 ( x ) !for! f ( x) = ln(2 − x) !centered!at!x!=!1.! ( ) ( ) ( ) ( ) n !!!!! ! k! ! \$\$\$\$\$ ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! f (a) ! f ( x) ! !! !! !! !! !! !! !! !! !! !! ! \$ k k !!!!!!!!!!! !! !! !! !! !! !! !! !! !! !! n =∑ f k (a) ! k! k =0 k f k ( a) ( x − a) k! Example!2:! Expand g( x ) = ! k! ! ! ! ! ! 2 in powers of (x - 1). x \$\$\$\$\$ \$ f (a) ! k k f ( x)...
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## This note was uploaded on 02/25/2014 for the course MATH 1432 taught by Professor Morgan during the Spring '08 term at University of Houston.

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