taylor 1/((1-3x^2)),x=0.577

Lösung

taylor

\frac{1}{( 1 - 3 x ^{2} )}, x = 0.577

824.40230 \dots + 2352910.79260 \dots (x - 0.577) + 6717436414.6027 (x - 0.577)^{2} + 1.91779 E 13 (x - 0.577)^{3} + \frac{1.64256 E 17}{3} (x - 0.577)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 824.40230 \dots + \frac{\frac{d}{d x} ( \frac{1}{1 - 3 x ^{2}} ) ( 0.577 )}{1 !} (x - 0.577) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - 3 x ^{2}} ) ( 0.577 )}{2 !} (x - 0.577)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - 3 x ^{2}} ) ( 0.577 )}{3 !} (x - 0.577)^{3} + \dots

Evaluate Derivatives

= 824.40230 \dots + \frac{2352910.79260 \dots}{1 !} (x - 0.577) + \frac{13434872829.2054}{2 !} (x - 0.577)^{2} + \frac{1.15068 E 14}{3 !} (x - 0.577)^{3} + \frac{1.31405 E 18}{4 !} (x - 0.577)^{4} + \dots

Fasse zusammen

= 824.40230 \dots + 2352910.79260 \dots (x - 0.577) + 6717436414.6027 (x - 0.577)^{2} + 1.91779 E 13 (x - 0.577)^{3} + \frac{1.64256 E 17}{3} (x - 0.577)^{4} + \dots