I have the following limit:
Since this leads to an indeterminate form $[0\cdot\infty]$, I change the variables:
$$t=\frac 1 x$$
The denominator grows faster than the nominator so the fraction tends to $0^+$. But since there is a minus there, I flip the value which becomes $0^-$. According to my textbook this is wrong. The limit is supposed to be $0^+$. Any hints on why my approach to get the $\pm$ is wrong?