taylor sin(pix),0.5

Lösung

taylor

sin (π x), 0.5

1 - 4.93480 \dots (x - 0.5)^{2} + 4.05871 \dots (x - 0.5)^{4} - 1.33526 \dots (x - 0.5)^{6} + 0.23533 \dots (x - 0.5)^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( sin ( π x ) ) ( 0.5 )}{1 !} (x - 0.5) + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( π x ) ) ( 0.5 )}{2 !} (x - 0.5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( π x ) ) ( 0.5 )}{3 !} (x - 0.5)^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} (x - 0.5) + \frac{- 9.86960 \dots}{2 !} (x - 0.5)^{2} + \frac{0}{3 !} (x - 0.5)^{3} + \frac{97.40909 \dots}{4 !} (x - 0.5)^{4} + \frac{0}{5 !} (x - 0.5)^{5} + \frac{- 961.38919 \dots}{6 !} (x - 0.5)^{6} + \frac{0}{7 !} (x - 0.5)^{7} + \frac{9488.53101 \dots}{8 !} (x - 0.5)^{8} + \dots

Fasse zusammen

= 1 - 4.93480 \dots (x - 0.5)^{2} + 4.05871 \dots (x - 0.5)^{4} - 1.33526 \dots (x - 0.5)^{6} + 0.23533 \dots (x - 0.5)^{8} + \dots

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