LaTeX 解答生成・検査パイプライン

実行日時: 2026-10-03T19:12:35（ID: 20261003-191235-bbbf02） ← 履歴一覧に戻る

¥begin{enumerate}

¥item 次の極限を求めよ。
¥begin{edaenumerate}
  ¥item $¥displaystyle ¥lim_{x ¥to 0} ¥dfrac{¥sin 3x}{4x}$
  ¥vspace{20ZW}
  ¥item $¥displaystyle ¥lim_{x ¥to 0} ¥dfrac{x}{¥sin 2x}$
  ¥vspace{20ZW}
  ¥item $¥displaystyle ¥lim_{x ¥to 0} ¥dfrac{¥sin 3x}{¥tan 2x}$
  ¥vspace{20ZW}
  ¥item $¥displaystyle ¥lim_{x ¥to 0} ¥dfrac{x^2}{1-¥cos 2x}$
  ¥vspace{20ZW}
  ¥item $¥displaystyle ¥lim_{x ¥to 0} ¥dfrac{1-¥cos x}{¥tan x}$
  ¥vspace{20ZW}
  ¥item $¥displaystyle ¥lim_{x ¥to 0} ¥dfrac{1- ¥cos x}{1-¥cos ¥left( ¥dfrac{1}{3} x ¥right)}$
  ¥vspace{20ZW}
  ¥item $¥displaystyle ¥lim_{x ¥to ¥pi} ¥dfrac{¥sin x}{x-¥pi}$
  ¥item $¥displaystyle ¥lim_{x ¥to 0} ¥dfrac{x}{¥tan 3x}$
¥end{edaenumerate}


¥item $0 ¥leqq ¥theta<2 ¥pi$のとき、次の方程式・不等式を解け。
¥begin{edaenumerate}
  ¥item $¥cos 2 ¥theta-¥sin ¥theta=0$¥vspace{25ZW}
  ¥item $¥sin 2 ¥theta-¥cos ¥theta>0$¥vspace{25ZW}
  ¥item $¥cos ¥theta-5 ¥cos ¥dfrac{¥theta}{2}+3=0$¥vspace{20ZW}
  ¥item $2 ¥sin 2 ¥theta+2 ¥sin ¥theta-2 ¥cos ¥theta-1=0$¥vspace{20ZW}
  
  ¥newpage
  
  ¥item $¥cos 3 ¥theta+¥cos 2 ¥theta+¥cos ¥theta=0$¥vspace{30ZW}
  ¥item $¥sin ¥theta+¥sqrt{3} ¥cos ¥theta=1$¥vspace{30ZW}
  ¥item $¥sin 2 ¥theta-¥cos 2 ¥theta ¥geqq 1$¥vspace{20ZW}
  ¥item $¥cos ¥theta+¥cos 3 ¥theta+¥cos 5 ¥theta=0$
  
  ¥newpage

  ¥item $¥cos ¥left( 2 ¥theta -¥dfrac{¥pi}{4} ¥right) > ¥dfrac{¥sqrt{3}}{2}$¥vspace{30ZW}
  ¥item $¥cos ¥left(¥dfrac{1}{2}¥theta - ¥dfrac{¥pi}{3} ¥right) ¥LEQQ ¥dfrac{1}{¥sqrt{2}}$¥vspace{20ZW}
  ¥item $¥tan ¥left(3 ¥theta -¥dfrac{¥pi}{3} ¥right) ¥LEQQ ¥sqrt{3}$¥vspace{20ZW}
  ¥item $¥sqrt{2} (¥sin ¥theta + ¥cos ¥theta ) >1$¥vspace{30ZW}
  ¥item $¥sin{2¥theta}-¥sqrt{3}¥cos{2¥theta}<1$
  ¥item $3¥sin{¥theta}+¥sqrt{7}¥cos{¥theta}<8$
  
¥end{edaenumerate}

¥end{enumerate}

\begin{enumerate}

\item
\begin{edaenumerate}
  \item $\dfrac{3}{4}$
  \item $\dfrac{1}{2}$
  \item $\dfrac{3}{2}$
  \item $\dfrac{1}{2}$
  \item $0$
  \item $9$
  \item $-1$
  \item $\dfrac{1}{3}$
\end{edaenumerate}

\item
\begin{edaenumerate}
  \item $\theta=\dfrac{\pi}{6},\ \dfrac{5\pi}{6},\ \dfrac{3\pi}{2}$
  \item $\dfrac{\pi}{6}<\theta<\dfrac{\pi}{2},\quad \dfrac{5\pi}{6}<\theta<\dfrac{3\pi}{2}$
  \item $\theta=\dfrac{2\pi}{3}$
  \item $\theta=\dfrac{\pi}{6},\ \dfrac{2\pi}{3},\ \dfrac{5\pi}{6},\ \dfrac{4\pi}{3}$
  \item $\theta=\dfrac{\pi}{4},\ \dfrac{2\pi}{3},\ \dfrac{3\pi}{4},\ \dfrac{5\pi}{4},\ \dfrac{4\pi}{3},\ \dfrac{7\pi}{4}$
  \item $\theta=\dfrac{\pi}{2},\ \dfrac{11\pi}{6}$
  \item $\dfrac{\pi}{4}\leqq\theta\leqq\dfrac{\pi}{2},\quad \dfrac{5\pi}{4}\leqq\theta\leqq\dfrac{3\pi}{2}$
  \item $\theta=\dfrac{\pi}{6},\ \dfrac{\pi}{3},\ \dfrac{\pi}{2},\ \dfrac{2\pi}{3},\ \dfrac{5\pi}{6},\ \dfrac{7\pi}{6},\ \dfrac{4\pi}{3},\ \dfrac{3\pi}{2},\ \dfrac{5\pi}{3},\ \dfrac{11\pi}{6}$
  \item $\dfrac{\pi}{24}<\theta<\dfrac{5\pi}{24},\quad \dfrac{25\pi}{24}<\theta<\dfrac{29\pi}{24}$
  \item $0\leqq\theta\leqq\dfrac{\pi}{6},\quad \dfrac{7\pi}{6}\leqq\theta<2\pi$
  \item $\theta\in\left[0,\dfrac{2\pi}{9}\right]\cup\left(\dfrac{5\pi}{18},\dfrac{5\pi}{9}\right]\cup\left(\dfrac{11\pi}{18},\dfrac{8\pi}{9}\right]\cup\left(\dfrac{17\pi}{18},\dfrac{11\pi}{9}\right]\cup\left(\dfrac{23\pi}{18},\dfrac{14\pi}{9}\right]\cup\left(\dfrac{29\pi}{18},\dfrac{17\pi}{9}\right]\cup\left(\dfrac{35\pi}{18},2\pi\right)$
  \item $0\leqq\theta<\dfrac{7\pi}{12},\quad \dfrac{23\pi}{12}<\theta<2\pi$
  \item $\theta\in\left[0,\dfrac{\pi}{4}\right)\cup\left(\dfrac{7\pi}{12},\dfrac{5\pi}{4}\right)\cup\left(\dfrac{19\pi}{12},2\pi\right)$
  \item $0\leqq\theta<2\pi$
\end{edaenumerate}

\end{enumerate}

誤りなし

\begin{enumerate}

\item
\begin{edaenumerate}
  \item $\dfrac{3}{4}$
  \item $\dfrac{1}{2}$
  \item $\dfrac{3}{2}$
  \item $\dfrac{1}{2}$
  \item $0$
  \item $9$
  \item $-1$
  \item $\dfrac{1}{3}$
\end{edaenumerate}

\item
\begin{edaenumerate}
  \item $\theta=\dfrac{\pi}{6},\ \dfrac{5\pi}{6},\ \dfrac{3\pi}{2}$
  \item $\dfrac{\pi}{6}<\theta<\dfrac{\pi}{2},\quad \dfrac{5\pi}{6}<\theta<\dfrac{3\pi}{2}$
  \item $\theta=\dfrac{2\pi}{3}$
  \item $\theta=\dfrac{\pi}{6},\ \dfrac{2\pi}{3},\ \dfrac{5\pi}{6},\ \dfrac{4\pi}{3}$
  \item $\theta=\dfrac{\pi}{4},\ \dfrac{2\pi}{3},\ \dfrac{3\pi}{4},\ \dfrac{5\pi}{4},\ \dfrac{4\pi}{3},\ \dfrac{7\pi}{4}$
  \item $\theta=\dfrac{\pi}{2},\ \dfrac{11\pi}{6}$
  \item $\dfrac{\pi}{4}\leqq\theta\leqq\dfrac{\pi}{2},\quad \dfrac{5\pi}{4}\leqq\theta\leqq\dfrac{3\pi}{2}$
  \item $\theta=\dfrac{\pi}{6},\ \dfrac{\pi}{3},\ \dfrac{\pi}{2},\ \dfrac{2\pi}{3},\ \dfrac{5\pi}{6},\ \dfrac{7\pi}{6},\ \dfrac{4\pi}{3},\ \dfrac{3\pi}{2},\ \dfrac{5\pi}{3},\ \dfrac{11\pi}{6}$
  \item $\dfrac{\pi}{24}<\theta<\dfrac{5\pi}{24},\quad \dfrac{25\pi}{24}<\theta<\dfrac{29\pi}{24}$
  \item $0\leqq\theta\leqq\dfrac{\pi}{6},\quad \dfrac{7\pi}{6}\leqq\theta<2\pi$
  \item $\theta\in\left[0,\dfrac{2\pi}{9}\right]\cup\left(\dfrac{5\pi}{18},\dfrac{5\pi}{9}\right]\cup\left(\dfrac{11\pi}{18},\dfrac{8\pi}{9}\right]\cup\left(\dfrac{17\pi}{18},\dfrac{11\pi}{9}\right]\cup\left(\dfrac{23\pi}{18},\dfrac{14\pi}{9}\right]\cup\left(\dfrac{29\pi}{18},\dfrac{17\pi}{9}\right]\cup\left(\dfrac{35\pi}{18},2\pi\right)$
  \item $0\leqq\theta<\dfrac{7\pi}{12},\quad \dfrac{23\pi}{12}<\theta<2\pi$
  \item $\theta\in\left[0,\dfrac{\pi}{4}\right)\cup\left(\dfrac{7\pi}{12},\dfrac{5\pi}{4}\right)\cup\left(\dfrac{19\pi}{12},2\pi\right)$
  \item $0\leqq\theta<2\pi$
\end{edaenumerate}

\end{enumerate}