taylor 1/((x+1)^2)

Lösung

taylor

\frac{1}{( x + 1 ) ^{2}}

1 - 2 x + 3 x^{2} - 4 x^{3} + 5 x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 2}{1 !} x + \frac{6}{2 !} x^{2} + \frac{- 24}{3 !} x^{3} + \frac{120}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - 2 x + 3 x^{2} - 4 x^{3} + 5 x^{4} + \dots

d er i v a t i v e f (x) = (- x^{2} + 4)^{2}

t an g e n t y = \frac{2}{x - 2} (4.1)

x \to 0 + lim ((2 x)^{5 x})

\int \frac{1}{y ^{2}} d y

x \to 3 lim (\frac{8}{x - 3})