taylor e^x+e^{-x}

Lösung

taylor

e^{x} + e^{- x}

2 + x^{2} + \frac{1}{12} x^{4} + \frac{1}{360} x^{6} + \frac{1}{20160} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{2}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{2}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{2}{8 !} x^{8} + \dots

Fasse zusammen

= 2 + x^{2} + \frac{1}{12} x^{4} + \frac{1}{360} x^{6} + \frac{1}{20160} x^{8} + \dots