calculus - Limits - Indeterminate forms

I have struggled with understanding indeterminate forms for quite sometime now. In this post, I put forward my understanding and hope to see it expand( or get corrected ).

Some limits of functions are certain at first observation, others are not. These "others", at a first look, take indeterminate forms as the independent variable gets sufficiently close to a point. By first look, I mean that an indeterminate form may crop up when we make a direct substitution in potential functions. We see that their limits take the following forms.

$0^0$; $1^\infty$; $0.\infty$; $\frac{\infty}{\infty}$; $\infty - \infty$; $\frac{0}{0}$

The term indeterminate, if I understand well, means that we are still not sure what the original value is( original limit as per the context of this post ). The original limit could be any real number, infinity or undefined( does not exist ). To properly convey this concept, I have constructed some examples. I shall deal with the above cases.

1) $0^0$

$\lim_{x\rightarrow 0} x^0 = 1$; $\lim_{x\rightarrow 0} 0^{|x|} =0$.

At first look, the above two limits take indeterminate forms. Their limits, however, are different. This tells us that an indeterminate form can take multiple real values.

2) $\frac{0}{0}$

$\lim_{x\rightarrow 0}\frac{\sin(x)}{x}=1$; $\lim_{x\rightarrow 0}\frac{|x|}{x}$ is undefined.

While both the limits take indeterminate forms at first look, the first takes a real value and the second's limit is undefined.

3) $1^\infty$

$\lim_{x\rightarrow 1} x^{\frac{1}{x-1}}=e$; $\lim_{x\rightarrow 1} x^{\frac{1}{|x-1|}}$ does not exist.

4) $\frac{\infty}{\infty}$

$\lim_{x\rightarrow 0} \frac{\frac{1}{x}}{\frac{1}{x}}=1$; $\lim_{x\rightarrow 0} \frac{\frac{1}{|x|}}{\frac{1}{x}}$ does not exist.

5) $0.\infty$

$\lim_{x\rightarrow 0} x.\frac{1}{x}=1$; $\lim_{x\rightarrow 0} \sin(x).\frac{1}{|x|}$ does not exist.

6) $\infty - \infty$

$\lim_{x\rightarrow 0} \frac{1}{x}-\frac{1}{x}=0$; $\lim_{x\rightarrow 0} \frac{1}{x}-\frac{1}{|x|}$ does not exist.

From the above, we see that indeterminate forms can take several values. Often while computing limits, we run into these forms. We then perform algebraic manipulations to arrive at the original limit( could exist or could not exist ). I haven't stated an Infinite limit in my examples. The following is one.

$\lim_{x\rightarrow 0} \frac{x}{x^2}$ is an infinite limit that, at first look, takes the indeterminate form $\frac{0}{0}$.

I end this post with a question. Are there other indeterminate forms?