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general power

base of the power, base, exponent, branch
complex power
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Mathematics Subject Classification

30D30 no label found


Anilped, you have requested unusual examples of limits of composite functions.
When x --> 0,
we have (1+1/x)^x --> 1.
Swapping the inner and the outer function,
we get 1+1/x^x --> 2.
Do you mean such cases?

The answer looks correct, but what do you mean by 'Swapping the inner and the outer function' ?

Now, when I read anew the request of anilped, I see that my examples do not answer to it.

How about f(x)=g(x)=1/x. Then the limit as x->0 of f(x) and g(x) does not exist yet the limit as x->0 of f(g(x)) is equal to 0.

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