taylor 4ln(7+2x^2)

Lösung

taylor

4 ln (7 + 2 x^{2})

4 ln (7) + \frac{8}{7} x^{2} - \frac{8}{49} x^{4} + \frac{32}{1029} x^{6} - \frac{16}{2401} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 4 ln (7) + \frac{\frac{d}{d x} ( 4 ln ( 7 + 2 x ^{2} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 4 ln ( 7 + 2 x ^{2} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 4 ln ( 7 + 2 x ^{2} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 4 ln (7) + \frac{0}{1 !} x + \frac{\frac{16}{7}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- \frac{192}{49}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{\frac{7680}{343}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- \frac{92160}{343}}{8 !} x^{8} + \dots

Fasse zusammen

= 4 ln (7) + \frac{8}{7} x^{2} - \frac{8}{49} x^{4} + \frac{32}{1029} x^{6} - \frac{16}{2401} x^{8} + \dots

f (x) = \frac{1}{x ^{6}}

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