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Firstly, how can we tell if the quotient is 0/0, or infinite/infinite, I know that obviously we can sub the variable in as 0 and if the result of both denominator and numerator is 0, we can apply the L'Hospital Rule.

But how can we tell whether its a 0/0 type or infinite/infinite type? And can we apply the rule if its a 0/infinite type or infinite/0 type?

2nd questions...

I just found out x = (1/(1/x)) Is this correct? Why is that so? How do you poof it? I know that x = 1/(x^-1) so if we invert it again... its 1/((1/(x)^-1))^-1 but how do you get (1/(1/x))?