Question

Question #e54a8

Answer 1

`lim_(xrarr0)x^2/lnx=0`

Explanation:

As `xrarr0`, `x^2rarr0` as well.

However, as `xrarr0`, we see that `lnxrarr-oo`.

Thus, as `xrarroo`, we see that the numerator of `x^2/lnx` becomes smaller and smaller and the denominator becomes larger and larger (in magnitude).

The limit, which can be seen as being in the "form" `0/oo`, then approaches `0`.

graph{x^2/lnx [-2, 5, -11.8, 13.86]}