I plugged in 1 for the f(x) I got:

\( 1-3x \over 1+x^2\)

As it approaches 0 \( 1-0 \over 1+0\)

Which simplifies to 1

I feel this is like very wrong :|

If \(\underset{x\rightarrow0}{lim}f(x)=1\), we have not indefinite case \(\frac{0}{0}\), so we have not a real problem, and we can't use for example the l'Hospital rule . We must have \(\underset{x\rightarrow0}{lim}f(x)=0.\)

Umm, so what do we do?