Lim nữa ....................................

Câu 91:

`lim_{x->+ oo} (\sqrt{x^{2} - 4x + 2} - x)`

`= lim_{x->+ oo} \frac{- 4x + 2}{\sqrt{x^{2} - 4x + 2} + x}`

`= lim_{x->+ oo} \frac{- 4 + \frac{2}{x}}{\sqrt{1 - \frac{4}{x} + \frac{2}{x^{2}}} + 1}`

`= \frac{- 4 + 0}{\sqrt{1 - 0 + 0} + 1}`

`= - 2`

`=>` Vậy đáp án đúng là B. - 2

Câu 92:

`I = lim_{x->+ oo} (x + 1 - \sqrt{x^{2} - x + 2})`

`= lim_{x->+ oo} (\frac{x - 2}{x + \sqrt{x^{2} - x + 2}} + 1)`

`= lim_{x->+ oo} (\frac{1 - \frac{2}{x}}{1 + \sqrt{1 - \frac{1}{x} + \frac{2}{x^{2}}}} + 1)`

`= \frac{1 - 0}{1 + \sqrt{1 - 0 + 2}} + 1`

`= \frac{1}{2} + 1`

`= \frac{3}{2}`

`=>` Vậy đáp án đúng là D. `I = \frac{3}{2}`

$\color{pink}{\text{$\textit{$\circ$ hungnguyen4269}$}}$

Đáp án:

`89)->D.1`

`lim_{x->+oo}(x+1-\root{3}{x^3+2})`$\\$ `=lim_{x->+oo}((x+1)^3-(\root{3}{x^3+2})^3)/((x+1)^2+(x+1)(\root{3}{x^3+2})+(\root{3}{x^3+2})^2)`$\\$ `=lim_{x->+oo}(x^3+3x^2+3x+1-x^3-2)/((x+1)^2+(x+1)(\root{3}{x^3+2})+(\root{3}{x^3+2})^2)`$\\$ `=lim_{x->+oo}(3x^2+3x-1)/((x+1)^2-(x+1)(\root{3}{x^3+2})+(\root{3}{x^3+2})^2)`$\\$ `=lim_{x->+oo}(x^2(3+3/x-1/x^2))/(x^2.(1+1/x)^2+x(1+1/x).x(\root{3}{1+2/x^3})+(x\root{3}{1+2/x^3})^2)`$\\$ `=lim_{x->+oo}(x^2(3+3/x-1/x^2))/(x^2.(1+1/x)^2+x^2(1+1/x)(\root{3}{1+2/x^3})+x^2(\root{3}{1+2/x^3})^2)`$\\$ `=lim_{x->+oo}(3+3/x-1/x^2)/((1+1/x)^2+(1+1/x)(\root{3}{1+2/x^3})+(\root{3}{1+2/x^3})^2)`$\\$ `=(3+0-0)/((1+0)^2+(1+0)(\root{3}{1+0})+(\root{3}{1+0})^2)`$\\$`=3/3=1`$\\$

`90)->D.7`

`lim_{x->-oo}(\sqrt{2x^2-3x+1}+x\sqrt{2})`$\\$ `=lim_{x->-oo}(2x^2-3x+1-2x^2)/(\sqrt{2x^2-3x+1}-x\sqrt{2})`$\\$ `=lim_{x->-oo}(-3x+1)/(\sqrt{2x^2-3x+1}-x\sqrt{2})`$\\$ `=lim_{x->-oo}(-x(3-1/x))/(-x\sqrt{2-3/x+1/x^2}-x\sqrt{2})`$\\$ `=lim_{x->-oo}(3-1/x)/(\sqrt{2-3/x+1/x^2}+\sqrt{2})`$\\$ `=(3-0)/(\sqrt{2-0+0}+\sqrt{2})`$\\$ `=3/(2\sqrt{2})=(3)/4.\sqrt{2}`$\\$ $\text{Với a,b $\in $ $\mathbb{Z}$ và $\dfrac{a}{b}$ tối giản}$`=> a=3,b=4`$\\$ `=>a+b=3+4=7`