taylor (9-x^2)^{-1/2}

Lösung

taylor

(9 - x^{2})^{- \frac{1}{2}}

\frac{1}{3} + \frac{1}{54} x^{2} + \frac{1}{648} x^{4} + \frac{5}{34992} x^{6} + \frac{35}{2519424} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{3} + \frac{\frac{d}{d x} ( ( 9 - x ^{2} ) ^{- \frac{1}{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 9 - x ^{2} ) ^{- \frac{1}{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 9 - x ^{2} ) ^{- \frac{1}{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{3} + \frac{0}{1 !} x + \frac{\frac{1}{27}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{1}{27}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{\frac{25}{243}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{1225}{2187}}{8 !} x^{8} + \dots

Fasse zusammen

= \frac{1}{3} + \frac{1}{54} x^{2} + \frac{1}{648} x^{4} + \frac{5}{34992} x^{6} + \frac{35}{2519424} x^{8} + \dots

t an g e n t y = 2 x^{2} + 9 x - 7

\frac{d}{d x} (2 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

f (x) = sec (x)

d er i v a t i v e y (θ) = \frac{π}{7} sin (θ)

x \to - 9 - lim (\frac{- 2 x}{x + 9})