[Calculus] L'Hospital's Rule || Lecture 37

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Today we learn L'Hospital's rule for finding limits.
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Isn't L'hospital meant to be used only in cases of 0/0, inf/inf ect.? Because in the first example of lim x->2 (lnx/(x-2)), x-2 is 0, but ln2 is not... and also the limit should not exist, it's -inf from the left and +inf from the right.

AnnieVictory