taylor (x^2+25)^{-3}

Lösung

taylor

(x^{2} + 25)^{- 3}

\frac{1}{15625} - \frac{3}{390625} x^{2} + \frac{6}{9765625} x^{4} - \frac{2}{48828125} x^{6} + \frac{3}{5 ^{13}} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{15625} + \frac{\frac{d}{d x} ( ( x ^{2} + 25 ) ^{- 3} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( x ^{2} + 25 ) ^{- 3} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( x ^{2} + 25 ) ^{- 3} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{15625} + \frac{0}{1 !} x + \frac{- \frac{6}{390625}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{144}{9765625}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{112500000}{2 5 ^{9}}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{236250000000}{2 5 ^{11}}}{8 !} x^{8} + \dots

Fasse zusammen

= \frac{1}{15625} - \frac{3}{390625} x^{2} + \frac{6}{9765625} x^{4} - \frac{2}{48828125} x^{6} + \frac{3}{5 ^{13}} x^{8} + \dots

x \to - 4 - lim (\frac{- 6 x}{x + 4})

d er i v a t i v e 3 cos (5 ln (x))

\frac{\partial}{\partial y} (4 x)

\int_{0}^{l n (12)} x e^{x} d x

x \to \infty lim ((1 + sin (6 x))^{\frac{1}{3 x}})