maclaurin sqrt(x^2-1)

Lösung

maclaurin

x^{2} - 1

i - \frac{i}{2} x^{2} - \frac{i}{8} x^{4} - \frac{i}{16} x^{6} - \frac{5 i}{128} x^{8} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= i + \frac{0}{1 !} x + \frac{- i}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 3 i}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 45 i}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 1575 i}{8 !} x^{8} + \dots

Fasse zusammen

= i - \frac{i}{2} x^{2} - \frac{i}{8} x^{4} - \frac{i}{16} x^{6} - \frac{5 i}{128} x^{8} + \dots

n = 2 \sum \infty \frac{1}{n ( n + 1 )}

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

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

\frac{d}{d x} (\frac{2}{x} - \frac{3 x}{3})

\frac{d}{d x} (\frac{x ^{3}}{4} + \frac{1}{3 x})