Lecture6and7

Lecture6and7 - h ee a id eh e e f a ia e h e e i facc ac gd...

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Unformatted text preview: h ee a id eh e e f a ia e h e e i facc ac gd ih ea i a i f ( x ) n summationdisplay k =0 f ( k ) ( x ) k ! ( x- x ) k ? ia h e ah c e i P n,x ( x ) f ( x ) ? e h eab ee i E = | f ( x )- P n,x ( x ) | b e b eab e ca c a eh ieac if ec dca c a e f ( x ) eac e d eed h e a i a i ! ead e eab iha ca ecea i ; e da ebd f E d h i eeg ig d e i eh ea ia i e a h e a ; e eeea d e ia i f75ad ac a i f74ad e ee ha C a chd id i8 F ihgh e ick e ie ac e f e eed b h ee i d ced ia h7 : h e iag e e a i h e ig ia e i i f ec : || a + b || || a || + || b || h i ih eea f h ea e ;eeF ig e if ec id ec i ea ec eb a iaa ia fh e i ea i f ca a : | a + b | | a | + | b | i fac a e hgh ie ea ha | a + b | ie ih eea | a | + | b | e e ih e ag id e fh ed iee ce : | | a | - | b | | h icaea ib ee ed ed a ge : | a 1 + a 2 + . . . + a n | | a 1 | + | a 2 | . . . + | a n | a ig h e e i i ea i h e ie a i h ed e i i f h ed e ie i eg a ee a h7 e ead h e f e eed :h e iag e ea i f eg a a eha vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle b a f ( x ) dx vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle b a | f ( x ) | dx. h icab ed ed i e fh e i e e a i fh ed e ie i eg a a aa ea ;eeF ig e ca eeha h i i e e a i e a eh e i eg a e id iec h eca a e i h eF d a e a h e e fC a c FC : a : d dx x a f ( t ) dt = f ( x ) a :if F prime ( x ) = f ( x ) h e b a f ( x ) dx = F ( b )- F ( a ) F ig e : F ig e : h eFCa i i fac a ig i f h id d e ia i fh e a ia ea iha i echage f...
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This note was uploaded on 04/05/2010 for the course MATH 119 taught by Professor Harmsworth during the Spring '08 term at Waterloo.

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Lecture6and7 - h ee a id eh e e f a ia e h e e i facc ac gd...

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