How do you find the limits?

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Indeterminate Forms

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Answer 1 · 2017-10-23T21:57:04

#e#

There exist a calculus book limit which is

#lim_(y->0)(1+y)^(1/y) = e#

In #lim_(x->0)(1+x+x^2)^(1/x)# when #x# is very small #x^2 << << x# so the contribution of #x^2# is discarded regarding #x# so

#lim_(x->0)(1+x+x^2)^(1/x) = lim_(x->0)(1+x)^(1/x) = e#