taylor ((x+1))/(x^2+1)

Lösung

taylor

\frac{( x + 1 )}{x ^{2} + 1}

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

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( \frac{x + 1}{x ^{2} + 1} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{x + 1}{x ^{2} + 1} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{x + 1}{x ^{2} + 1} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \dots

Fasse zusammen

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

\int 3 x^{\frac{5}{2}} - x^{\frac{5}{3}} d x

\int x sin (x^{2} + 5) d x

\int \frac{5}{6} x^{\frac{5}{6}} d x

f (x) = (1 - x^{2})^{\frac{1}{2}}

x \to - 1 + lim (\frac{1}{x + 1})