Evaluating $\lim_{x\to 0}\frac{3x^2}{4x^2}$ of $3x^2/4x^2 $
Is it undefined or $6/8$?
If we apply the Hospital rule we get $6/8$, so I think it is $6/8$.
It would be undefined if it were $3x^2/4x^3$.

Note that for all $x\neq 0$:
$$\frac{3x^2}{4x^2} = \frac{3}{4}.
$$
Hence then limit is
$$
\lim_{x\to 0}\;\frac{3x^2}{4x^2} = \lim_{x\to 0}\;\frac{3}{4} = \frac{3}{4}.
$$
This of course is the same as $\displaystyle{\frac{6}{8}}$.
The thing is that considering the limit you may assume that $x$ is not equal to zero.
