1. The problem statement, all variables and given/known data Use Taylor's theorem to estimate |(ex)-x-1| for 0≤x≤1. Thus prove that if a>(1/2) then: f(x)=(1-|x|a)*(ex)a is differentiable at x=0 2. Relevant equations 3. The attempt at a solution So |(ex)-x-1|=(x^2)/2+(x^3)/6+(x^4)/24... But I don't see how this helps, I have considered using the Lagrange remainder as well but again I can't see how that would help either. Any help would be greatly appreciated.