Bài tập 23 trang 31 SGK Toán 11 NC

Bài tập 23 trang 31 SGK Toán 11 NC

a) \(y = \frac{{1 - \cos x}}{{2\sin x + \sqrt 2 }}\) xác định \( \Leftrightarrow 2\sin x + \sqrt 2  \ne 0\)

\( \Leftrightarrow {\mathop{\rm sinx}\nolimits}  \ne  - \frac{{\sqrt 2 }}{2} \Leftrightarrow \left\{ \begin{array}{l}
x \ne  - \frac{\pi }{4} + k2\pi \\
x \ne \frac{{5\pi }}{4} + k2\pi 
\end{array} \right.\)

Vậy \(D = R\backslash \left( {\left\{ { - \frac{\pi }{4} + k2\pi ,k \in Z} \right\} \cup \left\{ {\frac{{5\pi }}{4} + k2\pi ,k \in Z} \right\}} \right)\)

b) \(y = \frac{{\sin \left( {x - 2} \right)}}{{\cos 2x - \cos x}}\) xác định \( \Leftrightarrow \cos 2x \ne \cos x\)

\(\begin{array}{l}
 \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
{2x \ne x + k2\pi }\\
{2x \ne  - x + k2\pi }
\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
{x \ne k2\pi }\\
{x \ne k\frac{{2\pi }}{3}}
\end{array}} \right.\\
 \Leftrightarrow x \ne k\frac{{2\pi }}{3}
\end{array}\)

Vậy \(D = R\backslash \left\{ {k\frac{{2\pi }}{3},k \in Z} \right\}\)

c)

\(y = \frac{{\tan x}}{{1 + \tan x}}\) xác định 

\( \Leftrightarrow \tan x \ne  - 1 \Leftrightarrow \left\{ \begin{array}{l}
x \ne \frac{\pi }{2} + k\pi \\
x \ne  - \frac{\pi }{4} + k\pi 
\end{array} \right.\)

Vậy \(D = R\backslash \left( {\left\{ {\frac{\pi }{2} + k\pi ,k \in Z} \right\} \cup \left\{ { - \frac{\pi }{4} + k\pi ,k \in Z} \right\}} \right)\)

d)

\(y = \frac{1}{{\sqrt 3 \cot 2x + 1}}\) xác định 

\( \Leftrightarrow \cot 2x \ne  - \frac{1}{{\sqrt 3 }}\)

\( \Leftrightarrow \left\{ \begin{array}{l}
2x \ne k\pi \\
2x \ne  - \frac{\pi }{3} + k\pi 
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne k\frac{\pi }{2}\\
x \ne  - \frac{\pi }{6} + k\frac{\pi }{2}
\end{array} \right.\)

Vậy \(D = R\backslash \left( {\left\{ {k\frac{\pi }{2},k \in Z} \right\} \cup \left\{ { - \frac{\pi }{6} + k\frac{\pi }{2},k \in Z} \right\}} \right)\)

-- Mod Toán 11