taylor sin(x),0.5

Lösung

taylor

sin (x), 0.5

0.47942 \dots + 0.87758 \dots (x - 0.5) - 0.23971 \dots (x - 0.5)^{2} - 0.14626 \dots (x - 0.5)^{3} + 0.01997 \dots (x - 0.5)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0.47942 \dots + \frac{\frac{d}{d x} ( sin ( x ) ) ( 0.5 )}{1 !} (x - 0.5) + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( x ) ) ( 0.5 )}{2 !} (x - 0.5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( x ) ) ( 0.5 )}{3 !} (x - 0.5)^{3} + \dots

Evaluate Derivatives

= 0.47942 \dots + \frac{0.87758 \dots}{1 !} (x - 0.5) + \frac{- 0.47942 \dots}{2 !} (x - 0.5)^{2} + \frac{- 0.87758 \dots}{3 !} (x - 0.5)^{3} + \frac{0.47942 \dots}{4 !} (x - 0.5)^{4} + \dots

Fasse zusammen

= 0.47942 \dots + 0.87758 \dots (x - 0.5) - 0.23971 \dots (x - 0.5)^{2} - 0.14626 \dots (x - 0.5)^{3} + 0.01997 \dots (x - 0.5)^{4} + \dots

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