x   =   1+\varepsilon x^{5}\\
f\left(x\right) =   1+\varepsilon x^{5}\\
    =   1+5\varepsilon^{4}x+10\varepsilon\\
f'\left(x\right)    =   5\varepsilon x^{4}\\
f''\left(x\right)   =   20\varepsilon x^{3}\\
    \thickapprox    1+\varepsilon\left(1+\varepsilon\right)^{5}