taylor 1/(sqrt(1-x^2)),0

Lösung

taylor

\frac{1}{1 - x ^{2}}, 0

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

Schritte zur Lösung

Apply the Taylor 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

a re a y = 2 x, y = x, x = 0, x = 4

t an g e n t f (x) = 5 - 2 x^{2}, (1, 3)

\frac{d}{d x} (7 e^{- x} - 8 e^{- 7 x})

t an g e n t f (x) = \frac{( x + 3 )}{2 x + 1}, at x = - 1

x \to 2 lim (\frac{1}{∣ x - 2 ∣})