An indeterminate form takes place if by knowing the limits of the functions involved we cannot determine what is the overall limit. We have to do a further analysis to solve this kind of situations.
If $$f(x)=x$$ and $$g(x)=\frac{1}{x}+1$$ then we know that $$\displaystyle\lim_{x \to{+}\infty}{f(x)}=+\infty$$ and $$\displaystyle\lim_{x \to{+}\infty}{g(x)}=1$$ but we cannot know beforehand the result of the limit $$\displaystyle\lim_{x \to{+}\infty}{g(x)^{f(x)}}=1^{+\infty}$$
The main indeterminate forms are: $$(+\infty)-(+\infty)$$, $$0 \cdot (\pm \infty)$$, $$\frac{0}{0}$$, $$(+\infty)^0$$, $$ 1^{\pm \infty}$$, $$0^0$$, $$ \frac{\pm \infty}{\pm \infty}$$ where all the values that appear are limits of functions.
Note that when we have things like: $$$\mbox{If } f(x) \to \infty \Rightarrow \left\{\begin{array}{r} \displaystyle\lim_{x \to{+}\infty}{1^{f(x)}}=\displaystyle\lim_{x \to{+}\infty}{1}=1 \\ \displaystyle\lim_{x \to{+}\infty}{\frac{0}{f(x)}}=\displaystyle\lim_{x \to{+}\infty}{0}=0 \\ \displaystyle\lim_{x \to{+}\infty}{f(x) \cdot 0}=\displaystyle\lim_{x \to{+}\infty}{0}=0 \\ \displaystyle\lim_{x \to{+}\infty}{\frac{0}{\frac{1}{f(x)}}}=\displaystyle\lim_{x \to{+}\infty}{0}=0 \end{array}\right.$$$ do not produce any indeterminate form.