Taylorpolynomier Funktion af flere variable
Taylorpolynomier Funktion af flere variable
Taylorpolynomier Funktion af flere variable
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<strong>Funktion</strong> givet ved simpel forskrift<br />
I f (x) = x arctan x med udviklingspunkt 1, orden 2.<br />
I Vi har<br />
f 0 (x) = arctan x + x<br />
1 + x 2<br />
f 00 2 2x<br />
(x) =<br />
2<br />
1 + x 2 (1 + x 2 ) 2<br />
I Så f (1) = π 4 , f 0 (1) = π 4 + 1 2 , f 00 (1) = 1 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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