taylor 1/(x^{1/2)}

Lösung

taylor

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

1 - \frac{1}{2} (x - 1) + \frac{3}{8} (x - 1)^{2} - \frac{5}{16} (x - 1)^{3} + \frac{35}{128} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- \frac{1}{2}}{1 !} (x - 1) + \frac{\frac{3}{4}}{2 !} (x - 1)^{2} + \frac{- \frac{15}{8}}{3 !} (x - 1)^{3} + \frac{\frac{105}{16}}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= 1 - \frac{1}{2} (x - 1) + \frac{3}{8} (x - 1)^{2} - \frac{5}{16} (x - 1)^{3} + \frac{35}{128} (x - 1)^{4} + \dots

t an g e n t f (x) = 2 x^{2} + x - 1, at x = 1

s l o p e (5.6) (6.9)

\int 2 r d r

d er i v a t i v e 7 ln (x)

y^{^{''}} + 3 y^{^{'}} + 4 y = 0