maclaurin sqrt(1-x)

Lösung

maclaurin

1 - x

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 Maclaurin 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^{^{''}} + 8 y^{^{'}} + 16 y = 1521 e^{2 t} cos (9 t)

l a pl a ce t r an s f or m cos^{2} (1 t)

t an g e n t f (x) = \frac{1}{x - 1}, at x = 5

\frac{d}{d x} (\frac{ln ( x )}{x ^{3}})

y^{^{'}} = 2 x y + x