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

Lösung

taylor

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

x^{2} + 2 x^{3} + 4 x^{4} + 8 x^{5} + 16 x^{6} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{12}{3 !} x^{3} + \frac{96}{4 !} x^{4} + \frac{960}{5 !} x^{5} + \frac{11520}{6 !} x^{6} + \dots

Fasse zusammen

= x^{2} + 2 x^{3} + 4 x^{4} + 8 x^{5} + 16 x^{6} + \dots

2 x^{^{''}} + 7 x^{^{'}} + 3 x = 0

t an g e n t f (x) = e^{5 x} cos (π x), at x = 0

d er i v a t i v e f (x) = x^{\frac{3}{2}}

d er i v a t i v e \frac{x ^{3}}{x ^{2} + 12}

y y^{^{'}} = 8 sin (x)