# general power

## Primary tabs

Defines:
base of the power, base, exponent, branch
Synonym:
complex power
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### anilped: unusual examples of limits

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?
Regards,
Jussi

### Re: anilped: unusual examples of limits

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

### Re: anilped: unusual examples of limits

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

### Re: anilped: unusual examples of limits

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.