Chọn B

\(\dfrac{1}{3}:\left(\dfrac{1}{6}-\dfrac{1}{2}\right)< =x< =\dfrac{2}{3}\left(-\dfrac{1}{6}+\dfrac{3}{4}\right)\)

=>\(\dfrac{1}{3}:\left(\dfrac{1}{6}-\dfrac{3}{6}\right)< =x< =\dfrac{2}{3}\left(-\dfrac{2}{12}+\dfrac{9}{12}\right)\)

=>\(\dfrac{1}{3}:\dfrac{-2}{6}< =x< =\dfrac{2}{3}\cdot\dfrac{7}{12}\)

=>\(\dfrac{1}{3}\cdot\dfrac{-6}{2}< =x< =\dfrac{14}{24}=\dfrac{7}{12}\)

=>\(-1< =x< =\dfrac{7}{12}\)

=>Chọn A

A

A

A

Câu 1: \(B.\frac{5}{8}\)

Câu 2: \(C.x=20;y=12\)

Câu 3: \(B.\frac{1}{4}\)

Do \(x-1\rightarrow0\) khi \(x\rightarrow1\) nên \(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-5}{x-1}=2\) hữu hạn khi và chỉ khi \(f\left(x\right)-5=0\) có nghiệm \(x=1\)

\(\Leftrightarrow f\left(1\right)-5=0\Rightarrow f\left(1\right)=5\)

Tương tự ta có \(g\left(1\right)=1\)

Do đó: \(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{f\left(x\right).g\left(x\right)+4}-3}{x-1}=\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right).g\left(x\right)-5}{\left(x-1\right)\left(\sqrt{f\left(x\right).g\left(x\right)+4}+3\right)}\)

\(=\lim\limits_{x\rightarrow1}\dfrac{\left[f\left(x\right)-5\right].g\left(x\right)+5\left[g\left(x\right)-1\right]}{\left(x-1\right)\left(\sqrt{f\left(x\right).g\left(x\right)+4}+3\right)}\)

\(=\left(2.1+5.3\right).\dfrac{1}{\sqrt{5.1+4}+3}=\dfrac{17}{6}\)

Ko có câu nào đúng

\(1-\dfrac{4}{x}+\dfrac{4}{x^2}=0\)

\(\Rightarrow\left(\dfrac{2}{x}-1\right)^2=0\)

\(\Rightarrow\dfrac{2}{x}=1\)

\(1-\dfrac{4}{x}+\dfrac{4}{x^2}=0\\ \Rightarrow\left(1-\dfrac{2}{x}\right)^2=0\\ \Rightarrow1-\dfrac{2}{x}=0\Rightarrow\dfrac{2}{x}=1\)