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Beliebt Rechnen >

taylor 4x^4+3x^3+2x^2+x+1,1

Lösung

taylor

4 x^{4} + 3 x^{3} + 2 x^{2} + x + 1, 1

Lösung

11 + 30 (x - 1) + 35 (x - 1)^{2} + 19 (x - 1)^{3} + 4 (x - 1)^{4}

Schritte zur Lösung

Apply the Taylor Formula

= 11 + \frac{\frac{d}{d x} ( 4 x ^{4} + 3 x ^{3} + 2 x ^{2} + x + 1 ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( 4 x ^{4} + 3 x ^{3} + 2 x ^{2} + x + 1 ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 4 x ^{4} + 3 x ^{3} + 2 x ^{2} + x + 1 ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 11 + \frac{30}{1 !} (x - 1) + \frac{70}{2 !} (x - 1)^{2} + \frac{114}{3 !} (x - 1)^{3} + \frac{96}{4 !} (x - 1)^{4}

Fasse zusammen

= 11 + 30 (x - 1) + 35 (x - 1)^{2} + 19 (x - 1)^{3} + 4 (x - 1)^{4}

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