Taylorpolynomier Funktion af flere variable
Taylorpolynomier Funktion af flere variable
Taylorpolynomier Funktion af flere variable
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Formlen for Taylorpolynomiet<br />
I Generelt fås altså<br />
således at<br />
a k = 1 k! f (k) (x 0 )<br />
P n (x) = f (x 0 ) + f 0 (x 0 ) (x x 0 ) + 1 2 f 00 (x 0 ) (x x 0 ) 2<br />
I Dette kan også skrives<br />
+ 1 3! f 000 (x 0 ) (x x 0 ) 3 + . . . + 1 n! f (n) (x 0 ) (x x 0 ) n<br />
P n (x) =<br />
n<br />
∑<br />
k=0<br />
1<br />
k! f (k) (x 0 ) (x x 0 ) k<br />
idet vi de…nerer 0! = 1 og f (0) = f .<br />
<strong>Taylorpolynomier</strong>.<br />
<strong>Funktion</strong> <strong>af</strong> ‡ere<br />
<strong>variable</strong><br />
Preben Alsholm<br />
<strong>Taylorpolynomier</strong><br />
De…nition <strong>af</strong><br />
Taylorpolynomium<br />
Udledning <strong>af</strong> formlen<br />
for Taylorpolynomiet<br />
Formlen for<br />
Taylorpolynomiet<br />
Eksempel 4.8.2 i<br />
Adams<br />
<strong>Funktion</strong> givet ved<br />
simpel forskrift<br />
<strong>Funktion</strong> givet ved<br />
di¤erentialligning<br />
Taylors formel med<br />
Lagrange’s restled<br />
Vurdering <strong>af</strong> fejlen<br />
ved Taylors formel I<br />
Vurdering <strong>af</strong> fejlen<br />
ved Taylors formel II<br />
Store O-notationen<br />
<strong>Funktion</strong> <strong>af</strong> ‡ere<br />
<strong>variable</strong>
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