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Homework Statement:

This is a famous problem of limit.
Lim ((1+x)^(1/x)e+ex/2)/x^2 where x tends to 0.
We can easily solve it with taylor expansion but i want to solve it without using taylor expansion.Is there a way?
Relevant Equations:
 Taylor expansion
I tried substituting x=cos2theta but it was of no use.I thought many ways but i could not make 0/0 form.So please help.