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Limits and Rate of Convergence (4 Problems)

Find Limits and Rate of Convergence.

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Ok, the idea is to expand the functions (Taylor Series) and then simplify:
1)
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 ...

Solution Summary

Limits and Rate of Convergence are investigated. The solution is detailed and well presented.

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