$= \mathop {\lim }\limits_{x \to +\infty } \sqrt{\frac{x^3(x^2+2x+1)}{2x^4+x^2+1}}$$= \mathop {\lim }\limits_{x \to +\infty } \sqrt{\frac{x^5+2x^4+x^3}{2x^4+x^2+1}}$$= \mathop {\lim }\limits_{x \to +\infty } \sqrt{\frac{x(\frac{1+\frac{2}{x}+\frac{1}{x^2}}}{2+\frac{1}{x^2}+\frac{1}{x^4}$$= \sqrt{+\infty . \frac{1}{2}}= +\infty$

$= \mathop {\lim }\limits_{x \to +\infty } \sqrt{\frac{x^3(x^2+2x+1)}{2x^4+x^2+1}}$$= \mathop {\lim }\limits_{x \to +\infty } \sqrt{\frac{x^5+2x^4+x^3}{2x^4+x^2+1}}$$= \mathop {\lim }\limits_{x \to +\infty } \sqrt{\frac{x(1+\frac{2}{x}+\frac{1}{x^2})}{2+\frac{1}{x^2}+\frac{1}{x^4}}}$$= \sqrt{+\infty . \frac{1}{2}}= +\infty$

c) Xét $lim (\sqrt{4n^2+3n+1}-2n) = lim \frac{3n+1}{\sqrt{4n^2+3n+1}+2n} = lim \frac{3+\frac{1}n}{\sqrt{4+\frac{3}n+\frac{1}{n^2}}+2} = \frac{3}{4}$$lim (\sqrt[3]{8n^3+2n-1} -2n)= lim \frac{2n-1}{\sqrt[3]{(8n^3+2n-1)^2}+2n.\sqrt[3]{8n^3+2n-1}+4n^2}= lim \frac{\frac{2}n - \frac{1}{n^2}}{\sqrt[3]{(8+\frac{2}{n^2}-\frac{1}{n^3})^2}+2.\sqrt[3]{8+\frac{2}{n^2}-\frac{1}{n^3}}+4}=\frac{0}{\sqrt[3]{64}+2.\sqrt[3]{8}+4}=0$vì $n \to + \infty \Rightarrow \frac{2}{n}-\frac{1}{n^2} >0$$\Rightarrow lim{\frac{2}n - \frac{1}{n^2}}{\sqrt[3]{(8+\frac{2}{n^2}-\frac{1}{n^3})^2}+2.\sqrt[3]{8+\frac{2}{n^2}-\frac{1}{n^3}}+4} = 0^+$$\Rightarrow lim \sqrt[3]{8n^3+2n-1}-2n = 0^+$$lim u_n=\frac{\frac{3}4}{0^+} = + \infty$

c) Xét $lim (\sqrt{4n^2+3n+1}-2n) = lim \frac{3n+1}{\sqrt{4n^2+3n+1}+2n} = lim \frac{3+\frac{1}n}{\sqrt{4+\frac{3}n+\frac{1}{n^2}}+2} = \frac{3}{4}$$lim (\sqrt[3]{8n^3+2n-1} -2n)= lim \frac{2n-1}{\sqrt[3]{(8n^3+2n-1)^2}+2n.\sqrt[3]{8n^3+2n-1}+4n^2}= lim \frac{\frac{2}n - \frac{1}{n^2}}{\sqrt[3]{(8+\frac{2}{n^2}-\frac{1}{n^3})^2}+2.\sqrt[3]{8+\frac{2}{n^2}-\frac{1}{n^3}}+4}=\frac{0}{\sqrt[3]{64}+2.\sqrt[3]{8}+4}=0$vì $n \to + \infty \Rightarrow \frac{2}{n}-\frac{1}{n^2} >0$$\Rightarrow lim \frac{\frac{2}n - \frac{1}{n^2}}{\sqrt[3]{(8+\frac{2}{n^2}-\frac{1}{n^3})^2}+2.\sqrt[3]{8+\frac{2}{n^2}-\frac{1}{n^3}}+4} = 0^+$$\Rightarrow lim \sqrt[3]{8n^3+2n-1}-2n = 0^+$ $lim u_n=\frac{\frac{3}4}{0^+} = + \infty$

giúp em với

1) cho x , y thỏa mãn 2x^{2} + y^{2} +xy \geq 1 . tìm \min của biểu thức A= x^{2} + y^{2}2) cho x , y thỏa mãn x^{2} + y^{2} = x^{2}y + xy^{2} . tìm \max và \min của biểu thứcA= \frac{2}{x} + \frac{1}{y}

GTLN, GTNN

giúp em với

1) cho x , y thỏa mãn $2x^{2} + y^{2} +xy \geq 1 .$ tìm \min của biểu thức $A= x^{2} + y^{2}$2) cho x , y thỏa mãn $x^{2} + y^{2} = x^{2}y + xy^{2} .$ tìm $\max$ và $\min$ của biểu thức $A= \frac{2}{x} + \frac{1}{y}$

GTLN, GTNN