taylor sqrt(1-x),0

Lösung

taylor

1 - x, 0

1 - \frac{1}{2} x - \frac{1}{8} x^{2} - \frac{1}{16} x^{3} - \frac{5}{128} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- \frac{1}{2}}{1 !} x + \frac{- \frac{1}{4}}{2 !} x^{2} + \frac{- \frac{3}{8}}{3 !} x^{3} + \frac{- \frac{15}{16}}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - \frac{1}{2} x - \frac{1}{8} x^{2} - \frac{1}{16} x^{3} - \frac{5}{128} x^{4} + \dots

y^{^{''}} + 3 y^{^{'}} + 2 y = cos (2 x)

a re a y = x, y = x^{3}, [- 1, 2]

\int - e^{2 t} d t

\frac{( 3 y ^{2} - t ^{2} )}{y ^{5}} \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

y^{^{'}} = y - x^{2} + 1, y (0) = 0