この問題には解答がありません。作成中ですのでしばらくお待ちください。
入試情報
大学名 |
京都府立医科大学 |
学科・方式 |
前期 |
年度 |
2008年度 |
問No |
問4 |
学部 |
医学部
|
カテゴリ |
図形と方程式 ・ 関数と極限
|
状態 |
 |
%
% すうじあむはアップするファイルで完結したTeXソースでないといけない.
% このひな形で表示確認をしよう.
%
\documentclass[b5paper,fleqn,papersize]{jsarticle}
%===========================================================
% ■余白の設定 B5
%-----------------------------------------------------------
\setlength{\oddsidemargin}{-5.4truemm} % 左マージン
\setlength{\topmargin}{-15.4truemm} % 上マージン
\setlength{\textwidth}{14.2cm} % B5 サイズ用
\setlength{\headheight}{2zw}
\setlength{\headsep}{2zw}
\setlength{\textheight}{217mm}
%===========================================================
\usepackage[dvipdfm]{graphicx,color}
%\usepackage{wallpaper}
\usepackage{wrapfig}
\usepackage{amsmath,amsthm,amssymb}
\usepackage{multicol}
\usepackage{longtable}
\usepackage{ascmac}
\usepackage{fancybox}
\usepackage{framed}
\usepackage{ifthen}
\usepackage{setspace} % setspaceパッケージのインクルード
\usepackage{amssymb}% ≒を表示するために必要
% \usepackage{comment}% コメント% mebio.styと競合する
\usepackage{booktabs}
\usepackage{ascmac}
\usepackage{itembbox}
%
% \usepackage{ custom_suseum}% すうじあむ
%=========================================================
%============================================================
% ■ 分数の横棒を長く,分数を立てに狭く(emath.styの古い記述)
%------------------------------------------------------------
% 分数記号(分数罫を少し長めに)
\newcommand{\bunsuu}[2]{\dfrac{\,#1\,}{\,#2\,}}%
% さらに罫線の上下を狭く.
\newcommand\Dfrac[2]{\bunsuu{\lower.6ex\hbox{$#1$}}{\lower-.3ex\hbox{$#2$}}}%
%============================================================
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% enumerate の自動ラベルの変更
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\labelenumi{(\theenumi)}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 増減表の矢印
% http://www.biwako.shiga-u.ac.jp/sensei/kumazawa/tex/arrow.html
%
% $\cvinc$ increase
% $\ccinc$ concavity 凹状の
% $\cvdec$ convex 凸形の
% $\ccdec$ decrease
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\makeatletter
\newcommand{\ccinc}{\ifx\@currsize\small
\setlength{\unitlength}{1.1pt}
\begin{picture}(10,10)(1,2)
\put(1,2){\line(0,1){3}}
\put(5,5){\oval(8,8)[lt]}
\put(5,9){\vector(1,0){4}}
\end{picture}\else
\setlength{\unitlength}{1.2pt}
\begin{picture}(10,10)(1,2)
\put(1,2){\line(0,1){3}}
\put(5,5){\oval(8,8)[lt]}
\put(5,9){\vector(1,0){4}}
\end{picture}\fi}
\newcommand{\cvinc}{\ifx\@currsize\small
\setlength{\unitlength}{1.1pt}
\begin{picture}(10,10)(2,1)
\put(2,1){\line(1,0){3}}
\put(5,5){\oval(8,8)[rb]}
\put(9,5){\vector(0,1){4}}
\end{picture}\else
\setlength{\unitlength}{1.2pt}
\begin{picture}(10,10)(2,1)
\put(2,1){\line(1,0){3}}
\put(5,5){\oval(8,8)[rb]}
\put(9,5){\vector(0,1){4}}
\end{picture}\fi}
\newcommand{\ccdec}{\ifx\@currsize\small
\setlength{\unitlength}{1.1pt}
\begin{picture}(10,10)(2,1)
\put(2,9){\line(1,0){3}}
\put(5,5){\oval(8,8)[rt]}
\put(9,5){\vector(0,-1){4}}
\end{picture}\else
\setlength{\unitlength}{1.2pt}
\begin{picture}(10,10)(2,1)
\put(2,9){\line(1,0){3}}
\put(5,5){\oval(8,8)[rt]}
\put(9,5){\vector(0,-1){4}}
\end{picture}\fi}
\newcommand{\cvdec}{\ifx\@currsize\small
\setlength{\unitlength}{1.1pt}
\begin{picture}(10,10)(1,0)
\put(1,8){\line(0,-1){3}}
\put(5,5){\oval(8,8)[lb]}
\put(5,1){\vector(1,0){4}}
\end{picture}\else
\setlength{\unitlength}{1.2pt}
\begin{picture}(10,10)(1,0)
\put(1,8){\line(0,-1){3}}
\put(5,5){\oval(8,8)[lb]}
\put(5,1){\vector(1,0){4}}
\end{picture}\fi}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%======================================================================
\newcommand{\解説印}{\fboxsep=1.3pt\noindent\ovalbox{\bf \,解\,説\,}\hspace{0.5em}}
% \newcommand{\解答印}{\fboxsep=1.3pt\noindent\fbox{\bf \,解\,答\,}\hspace{0.5em}}
\newcommand{\解答印}{\shadowsize=0.15\shadowsize{\fboxsep=1.3pt\noindent\shadowbox{\bf \,解\,答\,}\hspace{0.5em}}}
\newcommand{\別解印}{\fboxsep=1.3pt\noindent\fbox{\bf \,別\,解\,}\hspace{0.5em}}
\newcommand{\注意印}{\noindent{\bf [注意]}\hspace{0.5em}}
%======================================================================
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%■ベクトルの矢印の高さを揃える定義
% \overrightarrow の矢印の高さを揃える
% \vec, \Vec で定義する
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\vec#1{\overrightarrow{\mathstrut #1}}
\def\Vec#1{\overrightarrow{\mathstrut {\rm #1}}}
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%===========================================================
% ■二重根号
%-----------------------------------------------------------
\def\tsqrt#1{\textstyle\sqrt{#1}}
%===========================================================
%%% 平行 // の記号%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\para{%
\setlength{\unitlength}{1pt}%
\thinlines %
\begin{picture}(10, 12)%
\put(1,0){/}%
\put(4,0){/}%
\end{picture}%
}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%■ 答えを太文字
\newcommand{\kotae}[1]{\mbox{\boldmath$#1$}}
% \def\kotae#1{\mbox{\boldmath $#1$}}
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%===========================================================
% ■枠囲み
%-----------------------------------------------------------
\newcommand{\枠囲}[1]{\,\fboxsep1pt\fbox{ #1 }\,}% 文章中でも数式中でも使える?
% \newcommand{\枠}[1]{\fboxsep1pt\fbox{ #1 }\,}
%===========================================================
%===========================================================
% ■≦と≧の定義
%-----------------------------------------------------------
\def\le{\leqq}
\def\ge{\geqq}
\newcommand{\LEQQ}{\leqq}
\newcommand{\GEQQ}{\geqq}
% \newcommand{\LEQQ}{\mathrel{\mathpalette\gl@align<}}
% \newcommand{\GEQQ}{\mathrel{\mathpalette\gl@align>}}
% \newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
% \ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
% エラーになる。理由はよく解らん。
%===========================================================
%===========================================================
% ■行列 2×2
%-----------------------------------------------------------
\newcommand{\matrixTT}[4]{
\begin{pmatrix}
#1 & #2 \\
#3 & #4
\end{pmatrix}
}
%===========================================================
%===========================================================
% ■行列 3×3
%-----------------------------------------------------------
\newcommand{\matrixTTT}[9]{
\begin{pmatrix}
#1 & #2 & #3\\
#4 & #5 & #6\\
#7 & #8 & #9
\end{pmatrix}
}
%===========================================================
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ■ 3*1行列の定義
\newcommand{\matrixthreeone}[3]{
\left(\begin{array}{c}
#1\\
#2\\
#3
\end{array}\right)
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%===========================================================
% ■△ABCとか
%
% 「$\∠{ABC}=\Dfrac12\pi$」のような使い方をするので「$」は定義に含めない
%
%-----------------------------------------------------------
\def\△#1{\triangle{\rm #1}}
\def\∠#1{\angle{\rm #1}}
%===========================================================
%===========================================================
% ■角括弧 複数行 #1 は横幅%,#2は内容
%
%-----------------------------------------------------------
\newcommand{\角括弧}[2]{%
$%
\left[ \begin{tabular}{@{}p{.#1\linewidth}}#2\end{tabular} \right]%
$%
}
%===========================================================
%===========================================================
% ■丸括弧 複数行 #1 は横幅%,#2は内容
%-----------------------------------------------------------
\newcommand{\丸括弧}[2]{%
$%
\left( \begin{tabular}{@{}p{.#1\linewidth}}#2\end{tabular} \right)%
$%
}
%===========================================================
%===========================================================
% ■丸囲み数字 ①とか
%-----------------------------------------------------------
\newcommand{\tyoMaru}[1]{\mbox{{\normalsize \textcircled{\raisebox{-.25ex}{#1}}}}}
%===========================================================
%===========================================================
% ■ 微分 df/dt
%-----------------------------------------------------------
\newcommand{\dd}[2]{%
\dfrac{{\rm d}#1}{{\rm d}#2}%
}
%===========================================================
%===========================================================
% ■ ∫記号のdisplaystyleマクロ
%-----------------------------------------------------------
% \newcommand{\dint}{\displaystyle\int}% emathと干渉しないように\defで定義
\def\dint{\displaystyle\int}
%===========================================================
%===========================================================
% ■ Σ記号のdisplaystyleマクロ
%-----------------------------------------------------------
\newcommand{\dsum}{\displaystyle\sum}
%===========================================================
%===========================================================
% ■ lim記号のdisplaystyleマクロ
%-----------------------------------------------------------
\newcommand{\dlim}{\displaystyle\lim}
\newcommand{\Dsum}{\sum\limits}% ちっさいΣ
%===========================================================
%===========================================================
% ■ nCr マクロ
%-----------------------------------------------------------
\newcommand{\nCr}[2]{%
{}_{#1}\mathrm{C}_{#2}%
}
%===========================================================
%===========================================================
% ■ローマ数字 (i) (ii) (iii) (iv) (v) (vi) (vii) まで定義
%-----------------------------------------------------------
\providecommand{\RMi}{\mbox{(\hspace{.1em}i\hspace{.1em})}}
\providecommand{\RMii}{\mbox{(ii)}}
\providecommand{\RMiii}{\mbox{(i\hspace{-.1em}i\hspace{-.1em}i)}}
\providecommand{\RMiv}{\mbox{(i\hspace{-.1em}v)}}
\providecommand{\RMv}{\mbox{(\hspace{.1em}v\hspace{.1em})}}
\providecommand{\RMvi}{\mbox{(v\hspace{-.1em}i)}}
\providecommand{\RMvii}{\mbox{(\hspace{-.1em}v\hspace{-.1em}i\hspace{-.1em}i)}}
%===========================================================
%===========================================================
% ■点A(t, t^3)とか
% #1 は点の名前(「A」とか)
% #2 は「(t,\,t^3)」とか「(s,\,t,\,u)」と( )内を全部書く
% ()の大きさとか,の後のスペースとか微調整ができるように
%
%-----------------------------------------------------------
\providecommand{\点}[2]{${\rm#1} #2$}
%===========================================================
%===========================================================
% ■ 証明終了記号 ■
%-----------------------------------------------------------
\newcommand{\■}{{\tiny \text{■}}}
%===========================================================
\begin{document}
%%%%% ■ 本文開始 ■ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{FRAME}% この間に設問を書く% \usepackage{ custom_suseum} をゆうこうにすること
\begin{framed}
%
%----------------------------------------------------------------
$xy$平面上の点$(0,\ -1)$を中心とする半径2の円を$C$とおく.
第一象限に中心をもち,$C$に内接し,$x$軸に接する二つの円$A$,$B$を考える.
円$A$,$B$は互いに外接しているものとする.
円$A$の中心の$x$座標を$p$,半径を$r$,円$B$の中心の$x$座標を$q$,半径を$s$とし,
$p<q$をみたしているとする.
\begin{enumerate}
\item 極限値$\dlim_{p\to\sqrt{3}-0}\dfrac{\sqrt{3}-p}{r}$を求めよ.
\item 極限値$\dlim_{p\to\sqrt{3}-0}\dfrac{ \,s\, }{r}$を求めよ.
\end{enumerate}
%--------------------------------------------------------------
\end{framed}
%\end{FRAME}
%--- 解答 ------------------------------------------------------------------------
{\footnotesize
}% footnotesize
%%%%%%% ■ 本文終了 ■ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}