$d)\lim \dfrac{4^n}{7^n}{1+9.7^n}\\ =\lim \dfrac{\left(\dfrac{4}{7}\right)^n-1}{\dfrac{1}{7^n}+9}\\ = \dfrac{-1}{9}\\ e)2,(2)=2+\dfrac{2}{9}=\dfrac{20}{9}\\ 3,(03)=3+\dfrac{3}{99}=\dfrac{100}{33}\\ g)\lim \dfrac{4^{n+2}-3^{2n}}{5^n+9^n}\\ =\lim \dfrac{4.4^{n}-9^{n}}{5^n+9^n}\\ =\lim \dfrac{4.\left(\dfrac{4}{9}\right)^{n}-1}{\left(\dfrac{5}{9}\right)^n+1}\\ =-1$
