$\lim \left(\sqrt[3]{8n^3-13n}-\sqrt{4n^2-10n}\right)\\ =\lim \left(\sqrt[3]{8n^3-13n}-2n -\sqrt{4n^2-10n}+2n\right)\\ =\lim \left(\dfrac{\left(\sqrt[3]{8n^3-13n}-2n\right)\left(\sqrt[3]{8n^3-13n}^2+2n\sqrt[3]{8n^3-13n}+4n^2\right)}{\sqrt[3]{8n^3-13n}^2+2n\sqrt[3]{8n^3-13n}+4n^2} -\dfrac{\left(\sqrt{4n^2-10n}+2n\right)\left(\sqrt{4n^2-10n}-2n\right)}{\sqrt{4n^2-10n}+2n}\right)\\ =\lim \left(\dfrac{8n^3-13n-8n^3}{\sqrt[3]{8n^3-13n}^2+2n\sqrt[3]{8n^3-13n}+4n^2} -\dfrac{4n^2-10n-4n^2}{\sqrt{4n^2-10n}+2n}\right)\\ =\lim \left(\dfrac{-13n}{\sqrt[3]{8n^3-13n}^2+2n\sqrt[3]{8n^3-13n}+4n^2} +\dfrac{10n}{\sqrt{4n^2-10n}+2n}\right)\\ =\lim \left(\dfrac{\dfrac{-13}{n}}{\sqrt[3]{8-\dfrac{13}{n^2}}^2+2\sqrt[3]{8-\dfrac{13}{n^2}}+4} +\dfrac{10}{\sqrt{4-\dfrac{10}{n}}+2}\right)\\ $$ =\dfrac{10}{2+2}\\ =2,5\\ 2)\lim \dfrac{1+3+3^2+\cdots+3^n}{2^{n+2}-3^{n-2}}\\ =\lim \dfrac{\dfrac{3^{n+1}-1}{2}}{4.2^{n}-\dfrac{1}{3^3}.3^{n+1}}\\ =\lim \dfrac{3^{n+1}-1}{2\left(4.2^{n}-\dfrac{1}{3^3}3^{n+1}\right)}\\ =\lim \dfrac{1-\dfrac{1}{3^{n+1}}}{2\left(4.\left(\dfrac{2}{3}\right)^{n}-\dfrac{1}{27}\right)}\\ =\lim \dfrac{1}{-2\dfrac{1}{27}}\\ =-\dfrac{27}{2}$
