maclaurin 1/(1-x^2)

Lösung

maclaurin

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

1 + x^{2} + x^{4} + x^{6} + x^{8} + \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{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{40320}{8 !} x^{8} + \dots

Fasse zusammen

= 1 + x^{2} + x^{4} + x^{6} + x^{8} + \dots

t an g e n t y = x, (4, 2)

\frac{d}{d x} (3 x^{2} + 12 x + 9)

\int \frac{1}{36 e ^{- 5 x} + e ^{5 x}} d x

s l o p e in t erce pt (4) (8.8)

\int 9 (9 x + 2) d x