京都府立医科大学 前期 1993年度 問1

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大学名 京都府立医科大学
学科・方式 前期
年度 1993年度
問No 問1
学部 医学部
カテゴリ 数と式 ・ 二次関数
状態 解答なし 解説なし ウォッチリスト

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% % 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)} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 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 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\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}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %=========================================================== % ■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}% }% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %■ 答えを太文字 \newcommand{\kotae}[1]{\mbox{\boldmath$#1$}} % \def\kotae#1{\mbox{\boldmath $#1$}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %=========================================================== % ■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} % %---------------------------------------------------------------- % $m$を正の整数の定数とし, \[f(x)=-(m+1)x^2+(m^2+3)x\] とおく.変数$x$が整数値のみをとるとき,$f(x)$の最大値を求めよ. %-------------------------------------------------------------- \end{framed} %\end{FRAME} %--- 解答 ------------------------------------------------------------------------ {\footnotesize }% footnotesize %%%%%%% ■ 本文終了 ■ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document}