43.
ĐKXĐ: \(\left\{{}\begin{matrix}6-x>0\\log_2\left(6-x\right)\ge2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< 6\\6-x\ge4\end{matrix}\right.\) \(\Rightarrow x\le2\)
C là đáp án đúng
44.
Phương trình mặt cầu:
\(x^2+\left(y-1\right)^2+\left(z+1\right)^2=4\)
C là đáp án đúng
41.
\(log_{\dfrac{1}{2}}\left(x^2-3x+2\right)\ge-1\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2-3x+2>0\\x^2-3x+2\le2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x>2\\x< 1\end{matrix}\right.\\0\le x\le3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2< x\le3\\0\le x< 1\end{matrix}\right.\)
A là đáp án đúng
42.
\(\Leftrightarrow\left\{{}\begin{matrix}x-1>0\\11-2x>0\\-log_2\left(x-1\right)+log_2\left(11-2x\right)\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>1\\x< \dfrac{11}{2}\\log_2\left(\dfrac{11-2x}{x-1}\right)\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}1< x< \dfrac{11}{2}\\\dfrac{11-2x}{x-1}\ge1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}1< x< \dfrac{11}{2}\\\dfrac{12-3x}{x-1}\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}1< x< \dfrac{11}{2}\\1< x\le4\end{matrix}\right.\) \(\Rightarrow1< x\le4\)
B là đáp án đúng
39.
\(\int g\left(x\right)dx=\int\left(x+1\right)f'\left(x\right)dx\)
Đặt \(\left\{{}\begin{matrix}u=x+1\\dv=f'\left(x\right)dx\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}du=dx\\v=f\left(x\right)=\dfrac{x}{\sqrt{x^2+4}}\end{matrix}\right.\)
\(\Rightarrow I=\dfrac{x\left(x+1\right)}{\sqrt{x^2+4}}-\int\dfrac{x}{\sqrt{x^2+4}}dx=\dfrac{x^2+x}{\sqrt{x^2+4}}-\sqrt{x^2+4}+C\)
\(=\dfrac{x-4}{\sqrt{x^2+4}}+C\)
40.
\(\int\limits^3_1f\left(x\right)dx=\int\limits^2_1f\left(x\right)dx+\int\limits^3_2f\left(x\right)dx=-4+\left(-3\right)=-7\)
