taylor x^3+8x-1,-1

Lösung

taylor

x^{3} + 8 x - 1, - 1

- 10 + 11 (x + 1) - 3 (x + 1)^{2} + (x + 1)^{3}

Schritte zur Lösung

Apply the Taylor Formula

= - 10 + \frac{\frac{d}{d x} ( x ^{3} + 8 x - 1 ) ( - 1 )}{1 !} (x + 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{3} + 8 x - 1 ) ( - 1 )}{2 !} (x + 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{3} + 8 x - 1 ) ( - 1 )}{3 !} (x + 1)^{3} + \dots

Evaluate Derivatives

= - 10 + \frac{11}{1 !} (x + 1) + \frac{- 6}{2 !} (x + 1)^{2} + \frac{6}{3 !} (x + 1)^{3} + \frac{0}{4 !} (x + 1)^{4} + \frac{0}{5 !} (x + 1)^{5} + \frac{0}{6 !} (x + 1)^{6} + \frac{0}{7 !} (x + 1)^{7} + \frac{0}{8 !} (x + 1)^{8} + \frac{0}{9 !} (x + 1)^{9} + \frac{0}{10 !} (x + 1)^{10}

Fasse zusammen

= - 10 + 11 (x + 1) - 3 (x + 1)^{2} + (x + 1)^{3}