Regarding limits and $1^\infty$ 
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Why is $1^{\infty}$ considered to be an indeterminate form 

I have some questions about limits and the undefinability of $1^\infty$.
For example, is $\lim_{x\to\infty}1^x$ indefinite? Why is it not $1$? Or do mathematicians, when saying that $1^\infty$ is indefinite, actually refer to cases such as $lim_{x\to\infty} \left(1 + \frac{a}{x}\right)^x$ where even though at a first glace the result is $1$, this is actually a special case and it is equal to $e^a$?

When people say that $1^{\infty}$ is an indeterminate form, what they mean is that if $f(x)$ is a function such that $\lim_{x \to r} f(x) = 1$ and $g(x)$ is a function such that $\lim_{x \to r} g(x) = \infty$, the value of $\lim_{x \to r} f(x)^{g(x)}$ is not uniquely determined in general. It is determined in the special case that $f(x) = 1$, in which case the limit is obviously just $1$. 
