taylor x^4,1

Lösung

taylor

x^{4}, 1

1 + 4 (x - 1) + 6 (x - 1)^{2} + 4 (x - 1)^{3} + (x - 1)^{4}

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{4}{1 !} (x - 1) + \frac{12}{2 !} (x - 1)^{2} + \frac{24}{3 !} (x - 1)^{3} + \frac{24}{4 !} (x - 1)^{4}

Fasse zusammen

= 1 + 4 (x - 1) + 6 (x - 1)^{2} + 4 (x - 1)^{3} + (x - 1)^{4}

t an g e n t - \frac{2 x}{x ^{2} + 1}

\int_{0}^{l n (2)} s e^{s} d s

\frac{\partial}{\partial x} (\frac{2}{2 x + y})

x \to - 2 lim (- x^{2} + 4 x - 6)

t an g e n t f (x) = x^{2} + 1, (- 2, 5)