Taylorpolynomier Funktion af flere variable
Taylorpolynomier Funktion af flere variable
Taylorpolynomier Funktion af flere variable
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Udledning <strong>af</strong> formlen for Taylorpolynomiet<br />
I Vi ser med det samme, at a 0 = f (x 0 ). Da<br />
P 0 n (x) = a 1 + 2a 2 (x x 0 ) + 3a 3 (x x 0 ) 2<br />
I fås, at a 1 = f 0 (x 0 ). Da<br />
+4a 4 (x x 0 ) 3 + . . . + na n (x x 0 ) n 1<br />
P 00<br />
n (x) = 2a 2 + 3 2 a 3 (x x 0 ) + 4 3 a 4 (x x 0 ) 2<br />
+ . . . + n (n 1) a n (x x 0 ) n 2<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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