[tex]\lim_{n \to \infty} \frac{{a}^{\frac{1}{n^2+1}}-1}{\frac{1}{n^2+1}}}\frac{n^2}{n^2+1} +\frac{{b}^{\frac{1}{n^2+1}}-1}{\frac{1}{n^2+1}}}\frac{n^2}{n^2+1}=1*lna+1*lnb=lna+lnb[/tex]
