Find Limits and Rate of Convergence.
Ok, the idea is to expand the functions (Taylor Series) and then simplify:
lim (e^(x)-1)/x= lim (1+x+x^2/2!+x^3/3!+...-1)/x= lim (x+x^2/2!+x^3/3!+...)/x=
lim (1+x/2!+x^2/3!+...)= 1
As we see above, after simplification we have: lim ...
Limits and Rate of Convergence are investigated. The solution is detailed and well presented.