taylor x^2cos(x),0.1

Lösung

taylor

x^{2} cos (x), 0.1

0.00995 \dots + 0.19800 \dots (x - 0.1) + 0.97006 \dots (x - 0.1)^{2} - 0.19916 \dots (x - 0.1)^{3} - 0.49375 \dots (x - 0.1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0.00995 \dots + \frac{\frac{d}{d x} ( x ^{2} cos ( x ) ) ( 0.1 )}{1 !} (x - 0.1) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{2} cos ( x ) ) ( 0.1 )}{2 !} (x - 0.1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{2} cos ( x ) ) ( 0.1 )}{3 !} (x - 0.1)^{3} + \dots

Evaluate Derivatives

= 0.00995 \dots + \frac{0.19800 \dots}{1 !} (x - 0.1) + \frac{1.94012 \dots}{2 !} (x - 0.1)^{2} + \frac{- 1.19500 \dots}{3 !} (x - 0.1)^{3} + \frac{- 11.85023 \dots}{4 !} (x - 0.1)^{4} + \dots

Fasse zusammen

= 0.00995 \dots + 0.19800 \dots (x - 0.1) + 0.97006 \dots (x - 0.1)^{2} - 0.19916 \dots (x - 0.1)^{3} - 0.49375 \dots (x - 0.1)^{4} + \dots

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