Bài tập 2 trang 65 sgk Toán 11 tập 1 Cánh diều: Tính các giới hạn sau:
a) $\lim\frac{5n+1}{2n}$;
b) $\lim\frac{6n^{2}+8n+1}{5n^{2}+3}$;
c) $\lim\frac{\sqrt{n^{2}+5n+3}}{6n+2}$;
d) $\lim(2-\frac{1}{3^{n}})$;
e) $\lim\frac{3^{n}+2^{n}}{4.3^{n}}$;
g) $\lim\frac{2+\frac{1}{n}}{3^{n}}$.
Bài Làm:
a) $\lim\frac{5n+1}{2n}=\lim\frac{5+\frac{1}{n}}{2}=\frac{5}{2}$;
b) $\lim\frac{6n^{2}+8n+1}{5n^{2}+3}=\lim\frac{6+\frac{8}{n}+\frac{1}{n^{2}}}{5+\frac{3}{n^{2}}}=\frac{6}{5}$;
c) $\lim\frac{\sqrt{n^{2}+5n+3}}{6n+2}=\lim\frac{n\sqrt{1+\frac{5}{n}+\frac{3}{n^{2}}}}{n(6+\frac{2}{n})}=\frac{1}{6}$;
d) $\lim(2-\frac{1}{3^{n}})=\lim2-\lim(\frac{1}{3})^{n}=2$;
e) $\lim\frac{3^{n}+2^{n}}{4.3^{n}}=\lim\frac{1+(\frac{2}{3})^{n}}{4}=\frac{1}{4}$;
g) $\lim\frac{2+\frac{1}{n}}{3^{n}}=\lim\frac{2+0}{+\infty}=0$.
