Em cần giúp bài gì em nhỉ?

\(#TyHM\)

\(\lim\limits_{x\rightarrow+\infty}\left(ax-\sqrt{x^2+bx+2}\right)=\lim\limits_{x\rightarrow+\infty}x\left(a-\sqrt{1+\dfrac{b}{x}+\dfrac{2}{x^2}}\right)\)

Nếu \(a\ne1\Rightarrow\lim\limits_{x\rightarrow+\infty}\left(a-\sqrt{1+\dfrac{b}{x}+\dfrac{2}{x^2}}\right)=a-1\ne0\)

\(\Rightarrow\lim\limits_{x\rightarrow+\infty}x\left(a-\sqrt{1+\dfrac{b}{x}+\dfrac{2}{x^2}}\right)=\infty\) ko thỏa mãn giả thiết \(=4\) (hữu hạn)

\(\Rightarrow a=1\)

\(\lim\limits_{x\rightarrow+\infty}\left(x-\sqrt{x^2+bx+2}\right)=\lim\limits_{x\rightarrow+\infty}\dfrac{-bx-2}{x+\sqrt{x^2+bx+2}}=\lim\limits_{x\rightarrow+\infty}\dfrac{-b-\dfrac{2}{x}}{1+\sqrt{1+\dfrac{b}{x}+\dfrac{2}{x^2}}}=-\dfrac{b}{2}\)

\(\Rightarrow-\dfrac{b}{2}=4\Rightarrow b=-8\)

\(21,\\ e,PT\Leftrightarrow\left|2x-5\right|=5-2x\Leftrightarrow\left[{}\begin{matrix}2x-5=5-2x\left(x\ge\dfrac{5}{2}\right)\\5-2x=5-2x\left(x< \dfrac{5}{2}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\left(tm\right)\\0x=0\left(tm\right)\end{matrix}\right.\\ \Leftrightarrow x\in R\\ f,\Leftrightarrow\left|x-\dfrac{1}{4}\right|=\dfrac{1}{4}-x\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{4}=\dfrac{1}{4}-x\left(x\ge\dfrac{1}{4}\right)\\\dfrac{1}{4}-x=\dfrac{1}{4}-x\left(x< \dfrac{1}{4}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\left(tm\right)\\0x=0\left(tm\right)\end{matrix}\right.\\ \Leftrightarrow x\in R\)

21.

Giới hạn đã cho hữu hạn khi và chỉ khi \(a=1\)

Khi đó:

\(\lim\limits_{x\rightarrow+\infty}\left(x-\sqrt{x^2+bx+2}\right)=\lim\limits_{x\rightarrow+\infty}\dfrac{x^2-\left(x^2+bx+2\right)}{x+\sqrt{x^2+bx+2}}=\lim\limits_{x\rightarrow+\infty}\dfrac{-bx-2}{x+\sqrt{x^2+bx+2}}\)

\(=\lim\limits_{x\rightarrow+\infty}\dfrac{-b-\dfrac{2}{x}}{1+\sqrt{1+\dfrac{b}{x}+\dfrac{2}{x^2}}}=\dfrac{-b}{2}\)

\(\Rightarrow-\dfrac{b}{2}=4\Rightarrow b=-8\)

\(\Rightarrow a+b=1-8=-7\)

22.

B sai, do các cạnh bên của chóp đều tạo với đáy các góc bằng nhau

21:

\(y'=\dfrac{\left(x^2-3x+5\right)'\left(x+2\right)-\left(x+2\right)'\left(x^2-3x+5\right)}{\left(x+2\right)^2}\)

\(=\dfrac{\left(2x-3\right)\left(x+2\right)-\left(x^2-3x+5\right)}{\left(x+2\right)^2}\)

\(=\dfrac{2x^2+4x-3x-6-x^2+3x-5}{\left(x+2\right)^2}=\dfrac{x^2+4x-11}{\left(x+2\right)^2}\)

17:

Khi x<>0 thì \(\lim\limits_{x\rightarrow0}f\left(x\right)=\lim\limits_{x\rightarrow0}\dfrac{1+4x-1}{\sqrt{1+4x}+1}\cdot\dfrac{1}{x}\)

\(=\lim\limits_{x\rightarrow0}\dfrac{4}{\sqrt{1+4x}+1}=\dfrac{4}{1+1}=\dfrac{4}{2}=2\)

=>Chọn B