taylor e^{-h}+e^h

Lösung

taylor

e^{- h} + e^{h}

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

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

d er i v a t i v e 20 (1 + e^{10 - t})^{- 1}

y^{^{'}} = 8 x y

\frac{\partial}{\partial x} (x^{4} + y^{2} - 4)

y^{^{''}} - y^{^{'}} - 2 y = e^{2 t}

\frac{d}{d t} (\frac{1}{t})