taylor sqrt((1-x^2))

Lösung

taylor

(1 - x^{2})

1 - \frac{1}{2} x^{2} - \frac{1}{8} x^{4} - \frac{1}{16} x^{6} - \frac{5}{128} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( 1 - x ^{2} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 1 - x ^{2} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 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{- 3}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 45}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 1575}{8 !} x^{8} + \dots

Fasse zusammen

= 1 - \frac{1}{2} x^{2} - \frac{1}{8} x^{4} - \frac{1}{16} x^{6} - \frac{5}{128} x^{8} + \dots