a) \(A=\frac{2n+1+3n-5-4n+5}{n-3}=\frac{n+1}{n-3}\)

b) \(A=\frac{n+1}{n-3}=\frac{n-3+4}{n-3}=1+\frac{4}{n-3}\)

Để A đạt giá trị nguyên thì \(\frac{4}{n-3}\)đạt giá trị nguyên <=> \(n-3\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)

Tới đây lập bảng tìm n.

khó quá

\(A=\frac{2n+1}{n-3}+\frac{3n-5}{n-3}-\frac{4n-5}{n-3}\)

\(=\frac{2n+1+3n-5-4n+5}{n-3}\)

\(=\frac{n+1}{n-3}\)

a) Để A là phân số thì \(n-3\ne0\)

\(\Leftrightarrow n\ne3\)

b) Để A là số nguyên thì \(n+1⋮n-3\)

Ta có n+1=n-3+4

=> 4 \(⋮\)n-3

=> n-3\(\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)

Ta có bảng

Đặt  \(A=\frac{2n+1}{n-3}+\frac{3n-5}{n-3}-\frac{4n-5}{n-3}=\frac{2n+1+3n-5-4n-5}{n-3}=\frac{n-9}{n-3}\)

a) Để A là một phân số thì \(n-3\ne0\)=> \(n\ne3\)

b) Ta có : \(A=\frac{2n+1}{n-3}+\frac{3n-5}{n-3}-\frac{4n-5}{n-3}=\frac{n-9}{n-3}=\frac{n-3-6}{n-3}=1-\frac{6}{n-3}\)

A có giá trị nguyên <=> \(n-3\in\left\{\pm1;\pm2;\pm3;\pm6\right\}\)

1.

\(\lim \frac{3n^2+5n+4}{2-n^2}=\lim \frac{\frac{3n^2+5n+4}{n^2}}{\frac{2-n^2}{n^2}}=\lim \frac{3+\frac{5}{n}+\frac{4}{n^2}}{\frac{2}{n^2}-1}=\frac{3}{-1}=-3\)

2.

\(\lim \frac{2n^3-4n^2+3n+7}{n^3-7n+5}=\lim \frac{\frac{2n^3-4n^2+3n+7}{n^3}}{\frac{n^3-7n+5}{n^3}}=\lim \frac{2-\frac{4}{n}+\frac{3}{n^2}+\frac{7}{n^3}}{1-\frac{7}{n^2}+\frac{5}{n^3}}=\frac{2}{1}=2\)

3.

\(\lim (\frac{2n^3}{2n^2+3}+\frac{1-5n^2}{5n+1})=\lim (n-\frac{3n}{2n^2+3}+\frac{1}{5}-n-\frac{1}{5n+1})\)

\(=\frac{1}{5}-\lim (\frac{3n}{2n^2+3}+\frac{1}{5n+1})=\frac{1}{5}-\lim (\frac{3}{2n+\frac{3}{n}}+\frac{1}{5n+1})=\frac{1}{5}-0=\frac{1}{5}\)

4.

\(\lim \frac{1+3^n}{4+3^n}=\lim (1-\frac{3}{4+3^n})=1-\lim \frac{3}{4+3^n}=1-0=1\)

5.

\(\lim \frac{4.3^n+7^{n+1}}{2.5^n+7^n}=\lim \frac{\frac{4.3^n+7^{n+1}}{7^n}}{\frac{2.5^n+7^n}{7^n}}\)

\(=\lim \frac{4.(\frac{3}{7})^n+7}{2.(\frac{5}{7})^n+1}=\frac{7}{1}=7\)