a. \(lim \frac{1+2.3^{n}-7^{n}}{5^{n}+2.7^{n}}=lim \frac{(\frac{1}{7})^{n}+2.(\frac{3}{7})^{n}-1}{(\frac{5}{7})^{n}+2}=\frac{-1}{2}\)
b. \(lim \frac{4^{n}+1+6^{n}+2}{5^{n}+8^{n}}=lim \frac{(\frac{1}{2})^{n}+(\frac{1}{8})^{n}+(\frac{3}{4})^{n}+\frac{2}{8^{n}}}{(\frac{5}{8})^{n}+1}=lim \frac{0}{1}=0\)
