taylor-1/x 2

Lösung

taylor

- \frac{1}{x} 2

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= - 2 + \frac{2}{1 !} (x - 1) + \frac{- 4}{2 !} (x - 1)^{2} + \frac{12}{3 !} (x - 1)^{3} + \frac{- 48}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

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

d er i v a t i v e y = \frac{x}{x ^{2} + 1}

s im pl i f y 3 x^{2} - \frac{1}{x}

t an g e n t f (x) = x^{2} + 2 x, at x = 34

x \to \infty lim (2^{x})

\int \frac{x ^{2} + 2 x - 1}{( x + 1 ) ( x + 2 ) ( x + 3 )} d x