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

Lösung

maclaurin

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

2 x - 2 x^{3} + 2 x^{5} - 2 x^{7} + 2 x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 12}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{240}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 10080}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{725760}{9 !} x^{9} + \dots

Fasse zusammen

= 2 x - 2 x^{3} + 2 x^{5} - 2 x^{7} + 2 x^{9} + \dots

a re a F (x) = ln (2 x), y = 0, y = 2

a re a 5 sin (x), 5 cos (2 x), 0, \frac{π}{2}

\int_{- 3}^{3} \frac{1}{2} (81 - x^{4}) d x

\frac{d}{d x} (25 x^{2} - 1)

x \to \frac{π}{4} lim (tan^{t a n (2 x)} (x))