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

Lösung

taylor

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

337 + 438 (x - 3) + 217 (x - 3)^{2} + 48 (x - 3)^{3} + 4 (x - 3)^{4}

Schritte zur Lösung

Apply the Taylor Formula

= 337 + \frac{\frac{d}{d x} ( 4 + x ^{2} + 4 x ^{4} ) ( 3 )}{1 !} (x - 3) + \frac{\frac{d ^{2}}{d x ^{2}} ( 4 + x ^{2} + 4 x ^{4} ) ( 3 )}{2 !} (x - 3)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 4 + x ^{2} + 4 x ^{4} ) ( 3 )}{3 !} (x - 3)^{3} + \dots

Evaluate Derivatives

= 337 + \frac{438}{1 !} (x - 3) + \frac{434}{2 !} (x - 3)^{2} + \frac{288}{3 !} (x - 3)^{3} + \frac{96}{4 !} (x - 3)^{4}

Fasse zusammen

= 337 + 438 (x - 3) + 217 (x - 3)^{2} + 48 (x - 3)^{3} + 4 (x - 3)^{4}

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