maclaurin 1/(sqrt(1-x^2))

Lösung

maclaurin

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

1 + \frac{1}{2} x^{2} + \frac{3}{8} x^{4} + \frac{5}{16} x^{6} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{1}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{9}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{225}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \dots

Fasse zusammen

= 1 + \frac{1}{2} x^{2} + \frac{3}{8} x^{4} + \frac{5}{16} x^{6} + \dots

f (x) = \frac{12}{x}

(4 + x) y^{^{'}} = 5 y

\int \frac{- 9}{3 x ^{5}} d x

\frac{d}{d x} (1 - x^{3})

x \to 0 lim (\frac{sec ( x ) tan ( x )}{x})