taylor (sqrt(1+x))/(sqrt(1-x))

Lösung

taylor

\frac{1 + x}{1 - x}

1 + x + \frac{1}{2} x^{2} + \frac{1}{2} x^{3} + \frac{3}{8} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{1}{2 !} x^{2} + \frac{3}{3 !} x^{3} + \frac{9}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + x + \frac{1}{2} x^{2} + \frac{1}{2} x^{3} + \frac{3}{8} x^{4} + \dots

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

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

f (x) = 5 tan (x)

\frac{d}{d x} (e cos (x))

d er i v a t i v e f (x) = - 5