taylor (x^2+4)^{-3}

Lösung

taylor

(x^{2} + 4)^{- 3}

\frac{1}{64} - \frac{3}{256} x^{2} + \frac{3}{512} x^{4} - \frac{5}{2048} x^{6} + \frac{15}{16384} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{64} + \frac{\frac{d}{d x} ( ( x ^{2} + 4 ) ^{- 3} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( x ^{2} + 4 ) ^{- 3} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( x ^{2} + 4 ) ^{- 3} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{64} + \frac{0}{1 !} x + \frac{- \frac{3}{128}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{9}{64}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{225}{128}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{4725}{128}}{8 !} x^{8} + \dots

Fasse zusammen

= \frac{1}{64} - \frac{3}{256} x^{2} + \frac{3}{512} x^{4} - \frac{5}{2048} x^{6} + \frac{15}{16384} x^{8} + \dots