[tex]\lim _{x\to \infty \:}\left(\frac{3^x-1}{3^x+1}\right)=\lim _{x\to \infty \:}\left(\frac{1-\frac{1}{3^x}}{1+\frac{1}{3^x}}\right)=\frac{\lim _{x\to \infty \:}\left(1-\frac{1}{3^x}\right)}{\lim _{x\to \infty \:}\left(1+\frac{1}{3^x}\right)}=\frac{1}{1}=1[/tex]