What is taylor e^{-h}+e^h ?

The answer to taylor e^{-h}+e^h is 2+h^2+1/12 h^4+1/360 h^6+1/20160 h^8+\ldots

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taylor e^{-h}+e^h

taylor

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

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

Solution steps

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

Refine

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

20 (1 + e^{10 - t})^{- 1}

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

\int \frac{4}{x ^{2} x ^{2} + 25} d x

y^{^{'}} + x^{- 1} y = - 2 x^{2} y^{2}, y (1) = \frac{1}{2}

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

What is taylor e^{-h}+e^h ?
The answer to taylor e^{-h}+e^h is 2+h^2+1/12 h^4+1/360 h^6+1/20160 h^8+\ldots