ヘルプ
数学博物館『すうじあむ』にようこそ。 『すうじあむ』は数学の問題・解答・解説のデータベースをはじめ 数学に関するあらゆる情報が詰まったポータルサイトです。
京都府立医科大学 前期 1995年度 問2
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。
- 閲覧数: 1051
- コメント数: 0
このコンテンツをご覧いただくためにはJavaScriptをONにし、最新のFlash Playerが必要です。
入試情報
| 大学名 | 京都府立医科大学 |
|---|---|
| 学科・方式 | 前期 |
| 年度 | 1995年度 |
| 問No | 問2 |
| 学部 | 医学部 |
| カテゴリ | 積分法 ・ 積分法の応用 |
| 状態 |    |
コメントをつけるにはログインが必要です。
コメントはまだありません。
タグをつけるにはログインが必要です。
%
% 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
\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}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%===========================================================
% ■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)}}
%===========================================================
%===========================================================
% ■minipage マクロ
%
% #1 左幅% #2 左内容 #3 右幅% #4 右内容
%
% \ミニ頁{左幅%}{左内容}{右幅%}{右内容}
%
%-----------------------------------------------------------
\providecommand{\ミニ頁}[4]{%
%
\noindent
\begin{minipage}[t]{.#1\linewidth}{\setlength{\parindent}{1\Cwd}%
\vspace{0mm}% ← これはない方がいいのかも
#2}
\end{minipage}
\begin{minipage}[t]{.#3\linewidth}{\setlength{\parindent}{1\Cwd}
\vspace{0mm}
#4}
\end{minipage}
}
% http://www2s.biglobe.ne.jp/~nuts/labo/inti/inti05.html
% minipage 環境では、変数 \parindent が 0\Cwd になるために起こる。
% インデントをつけたい minipage の始まり （\begin{minipage} の後）に、
% \setlength{\parindent}{1\Cwd} （これが通常時の値）と書けばよい。
% 私の記憶によれば、breakbox 環境内でも同じことが起こったように思う。
%===========================================================
%===========================================================
% ■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}
%
%----------------------------------------------------------------
%
$n$ は正の整数とする．円 $x^2+y^2-2y=0$ の中心をCとおく．\\
$k=0,\,1,\,2,\,\cdots,\,n$ に対して，点${\rm A}_k\left(\Dfrac{k}{n},\,0\right)$ をとり，
$\alpha_k=\angle{\rm A}_k{\rm CO}$ とする．\\
$\theta_k=\alpha_k-\alpha_{k-1}=\angle{\rm A}_{k-1}{\rm C}{\rm A}_k \ (k=1,\,2,\,\cdots,\,n)$
と定めるとき，\\
%
\ミニ頁{67}{%
\begin{enumerate}
\item $\Dfrac12\Dsum_{k=1}^n \sin\theta_k < \Dfrac{\pi}8<\Dfrac12\Dsum_{k=1}^n\tan\theta_k$ を示せ．
\item $k=0,\,1,\,2,\,\cdots,\,n$ に対して，次の2つの不等式を示せ．
\[\Dfrac1n\cdot\Dfrac1{1+\left(\Dfrac{k}{n}\right)^2}<\sin\theta_k\]
\[\tan\theta_k<\Dfrac1n\cdot\Dfrac1{1+\left(\Dfrac{k-1}{n}\right)^2}\]
\item 上の結果を用いて，$\dint_0^1\Dfrac1{1+x^2}dx$ を求めよ．
\end{enumerate}
}{26}{
\begin{center}
%WinTpicVersion4.28b
{\unitlength 0.1in
\begin{picture}( 14.4000, 14.4000)( 4.0000,-18.4000)
% STR 2 0 3 0 Black White
% 4 1114 1598 1114 1606 4 2400 0 0
% O
\put(11.1400,-16.0600){\makebox(0,0)[rt]{O}}%
% STR 2 0 3 0 Black White
% 4 1096 392 1096 400 4 2400 0 0
% $y$
\put(10.9600,-4.0000){\makebox(0,0)[rt]{$y$}}%
% STR 2 0 3 0 Black White
% 4 1840 1616 1840 1624 4 2400 0 0
% $x$
\put(18.4000,-16.2400){\makebox(0,0)[rt]{$x$}}%
% VECTOR 2 0 3 0 Black White
% 2 1120 1840 1120 400
%
{\color[named]{Black}{%
\special{pn 8}%
\special{pa 1120 1840}%
\special{pa 1120 400}%
\special{fp}%
\special{sh 1}%
\special{pa 1120 400}%
\special{pa 1100 468}%
\special{pa 1120 454}%
\special{pa 1140 468}%
\special{pa 1120 400}%
\special{fp}%
}}%
% VECTOR 2 0 3 0 Black White
% 2 400 1600 1840 1600
%
{\color[named]{Black}{%
\special{pn 8}%
\special{pa 400 1600}%
\special{pa 1840 1600}%
\special{fp}%
\special{sh 1}%
\special{pa 1840 1600}%
\special{pa 1774 1580}%
\special{pa 1788 1600}%
\special{pa 1774 1620}%
\special{pa 1840 1600}%
\special{fp}%
}}%
% FUNC 2 0 3 0 Black White
% 10 400 400 1840 1840 1120 1600 1600 1600 1120 1120 160 160 160 160 10 2 0 4 1 0
% ///x^2+y^2-2y=0///-2///2
{\color[named]{Black}{%
\special{pn 8}%
\special{pa 1500 1414}%
\special{pa 1502 1412}%
\special{pa 1502 1410}%
\special{pa 1506 1408}%
\special{pa 1506 1406}%
\special{pa 1508 1404}%
\special{pa 1508 1402}%
\special{pa 1512 1400}%
\special{pa 1512 1398}%
\special{pa 1516 1394}%
\special{pa 1516 1392}%
\special{pa 1518 1390}%
\special{pa 1518 1388}%
\special{pa 1522 1384}%
\special{pa 1524 1380}%
\special{pa 1528 1376}%
\special{pa 1528 1374}%
\special{pa 1530 1372}%
\special{pa 1530 1370}%
\special{pa 1532 1368}%
\special{pa 1534 1364}%
\special{pa 1536 1362}%
\special{pa 1536 1360}%
\special{pa 1540 1356}%
\special{pa 1540 1352}%
\special{pa 1542 1352}%
\special{pa 1542 1348}%
\special{pa 1544 1348}%
\special{pa 1544 1346}%
\special{pa 1546 1344}%
\special{pa 1546 1342}%
\special{pa 1548 1340}%
\special{pa 1548 1338}%
\special{pa 1550 1336}%
\special{pa 1550 1334}%
\special{pa 1552 1332}%
\special{pa 1552 1330}%
\special{pa 1554 1328}%
\special{pa 1554 1324}%
\special{pa 1556 1324}%
\special{pa 1556 1320}%
\special{pa 1558 1320}%
\special{pa 1558 1316}%
\special{pa 1560 1316}%
\special{pa 1560 1312}%
\special{pa 1562 1310}%
\special{pa 1562 1306}%
\special{pa 1564 1306}%
\special{pa 1564 1302}%
\special{pa 1566 1302}%
\special{pa 1566 1298}%
\special{pa 1568 1296}%
\special{pa 1568 1292}%
\special{pa 1570 1292}%
\special{pa 1570 1286}%
\special{pa 1572 1286}%
\special{pa 1572 1282}%
\special{pa 1574 1280}%
\special{pa 1574 1276}%
\special{pa 1576 1274}%
\special{pa 1576 1270}%
\special{pa 1578 1268}%
\special{pa 1578 1264}%
\special{pa 1580 1262}%
\special{pa 1580 1256}%
\special{pa 1582 1256}%
\special{pa 1582 1250}%
\special{pa 1584 1248}%
\special{pa 1584 1242}%
\special{pa 1586 1240}%
\special{pa 1586 1234}%
\special{pa 1588 1234}%
\special{pa 1588 1226}%
\special{pa 1590 1224}%
\special{pa 1590 1216}%
\special{pa 1592 1216}%
\special{pa 1592 1206}%
\special{pa 1594 1204}%
\special{pa 1594 1194}%
\special{pa 1596 1192}%
\special{pa 1596 1178}%
\special{pa 1598 1178}%
\special{pa 1598 1158}%
\special{pa 1600 1158}%
\special{pa 1600 1084}%
\special{pa 1598 1082}%
\special{pa 1598 1064}%
\special{pa 1596 1062}%
\special{pa 1596 1048}%
\special{pa 1594 1048}%
\special{pa 1594 1036}%
\special{pa 1592 1036}%
\special{pa 1592 1026}%
\special{pa 1590 1024}%
\special{pa 1590 1016}%
\special{pa 1588 1016}%
\special{pa 1588 1008}%
\special{pa 1586 1006}%
\special{pa 1586 1000}%
\special{pa 1584 1000}%
\special{pa 1584 992}%
\special{pa 1582 992}%
\special{pa 1582 986}%
\special{pa 1580 984}%
\special{pa 1580 978}%
\special{pa 1578 978}%
\special{pa 1578 972}%
\special{pa 1576 972}%
\special{pa 1576 966}%
\special{pa 1574 966}%
\special{pa 1574 960}%
\special{pa 1572 960}%
\special{pa 1572 958}%
\special{pa 1570 952}%
\special{pa 1570 950}%
\special{pa 1568 948}%
\special{pa 1568 944}%
\special{pa 1566 944}%
\special{pa 1566 940}%
\special{pa 1564 938}%
\special{pa 1564 936}%
\special{pa 1562 934}%
\special{pa 1562 932}%
\special{pa 1560 928}%
\special{pa 1560 926}%
\special{pa 1558 924}%
\special{pa 1558 922}%
\special{pa 1556 920}%
\special{pa 1556 918}%
\special{pa 1554 916}%
\special{pa 1554 914}%
\special{pa 1546 898}%
\special{pa 1546 896}%
\special{pa 1542 892}%
\special{pa 1542 890}%
\special{pa 1540 888}%
\special{pa 1540 886}%
\special{pa 1538 884}%
\special{pa 1536 880}%
\special{pa 1536 878}%
\special{pa 1530 872}%
\special{pa 1530 868}%
\special{pa 1526 864}%
\special{pa 1526 862}%
\special{pa 1520 856}%
\special{pa 1520 854}%
\special{pa 1518 852}%
\special{pa 1516 848}%
\special{pa 1514 846}%
\special{pa 1514 844}%
\special{pa 1508 838}%
\special{pa 1506 834}%
\special{pa 1502 830}%
\special{pa 1500 826}%
\special{pa 1496 822}%
\special{pa 1496 820}%
\special{pa 1480 804}%
\special{pa 1480 802}%
\special{pa 1470 792}%
\special{pa 1450 770}%
\special{pa 1448 770}%
\special{pa 1432 754}%
\special{pa 1430 754}%
\special{pa 1426 750}%
\special{pa 1424 750}%
\special{pa 1416 742}%
\special{pa 1414 742}%
\special{pa 1412 738}%
\special{pa 1410 738}%
\special{pa 1408 736}%
\special{pa 1406 736}%
\special{pa 1404 732}%
\special{pa 1402 732}%
\special{pa 1400 730}%
\special{pa 1398 730}%
\special{pa 1394 726}%
\special{pa 1392 726}%
\special{pa 1390 722}%
\special{pa 1388 722}%
\special{pa 1384 718}%
\special{pa 1380 718}%
\special{pa 1376 714}%
\special{pa 1374 714}%
\special{pa 1368 708}%
\special{pa 1364 708}%
\special{pa 1360 704}%
\special{pa 1358 704}%
\special{pa 1356 702}%
\special{pa 1348 698}%
\special{pa 1346 698}%
\special{pa 1342 694}%
\special{pa 1340 694}%
\special{pa 1338 692}%
\special{pa 1336 692}%
\special{pa 1334 690}%
\special{pa 1332 690}%
\special{pa 1330 688}%
\special{pa 1328 688}%
\special{pa 1326 686}%
\special{pa 1324 686}%
\special{pa 1316 682}%
\special{pa 1314 682}%
\special{pa 1312 680}%
\special{pa 1310 680}%
\special{pa 1308 678}%
\special{pa 1306 678}%
\special{pa 1302 676}%
\special{pa 1300 676}%
\special{pa 1298 674}%
\special{pa 1294 674}%
\special{pa 1294 672}%
\special{pa 1292 672}%
\special{pa 1286 670}%
\special{pa 1284 670}%
\special{pa 1282 668}%
\special{pa 1280 668}%
\special{pa 1276 666}%
\special{pa 1274 666}%
\special{pa 1270 664}%
\special{pa 1268 664}%
\special{pa 1264 662}%
\special{pa 1260 662}%
\special{pa 1258 660}%
\special{pa 1252 660}%
\special{pa 1252 658}%
\special{pa 1248 658}%
\special{pa 1242 656}%
\special{pa 1238 656}%
\special{pa 1238 654}%
\special{pa 1230 654}%
\special{pa 1228 652}%
\special{pa 1220 652}%
\special{pa 1220 650}%
\special{pa 1210 650}%
\special{pa 1210 648}%
\special{pa 1204 648}%
\special{pa 1194 646}%
\special{pa 1186 646}%
\special{pa 1186 644}%
\special{pa 1170 644}%
\special{pa 1168 642}%
\special{pa 1142 642}%
\special{pa 1142 640}%
\special{pa 1100 640}%
\special{pa 1098 642}%
\special{pa 1072 642}%
\special{pa 1072 644}%
\special{pa 1056 644}%
\special{pa 1054 646}%
\special{pa 1048 646}%
\special{pa 1036 648}%
\special{pa 1032 648}%
\special{pa 1030 650}%
\special{pa 1022 650}%
\special{pa 1020 652}%
\special{pa 1012 652}%
\special{pa 1012 654}%
\special{pa 1004 654}%
\special{pa 1002 656}%
\special{pa 1000 656}%
\special{pa 992 658}%
\special{pa 990 658}%
\special{pa 988 660}%
\special{pa 982 660}%
\special{pa 982 662}%
\special{pa 978 662}%
\special{pa 960 668}%
\special{pa 958 668}%
\special{pa 958 670}%
\special{pa 952 670}%
\special{pa 952 672}%
\special{pa 948 672}%
\special{pa 946 674}%
\special{pa 942 674}%
\special{pa 942 676}%
\special{pa 938 676}%
\special{pa 936 678}%
\special{pa 932 678}%
\special{pa 932 680}%
\special{pa 928 680}%
\special{pa 928 682}%
\special{pa 924 682}%
\special{pa 922 684}%
\special{pa 920 684}%
\special{pa 918 686}%
\special{pa 914 686}%
\special{pa 914 688}%
\special{pa 910 688}%
\special{pa 910 690}%
\special{pa 906 690}%
\special{pa 906 692}%
\special{pa 902 692}%
\special{pa 902 694}%
\special{pa 898 694}%
\special{pa 898 696}%
\special{pa 896 696}%
\special{pa 894 698}%
\special{pa 892 698}%
\special{pa 890 700}%
\special{pa 888 700}%
\special{pa 884 704}%
\special{pa 880 704}%
\special{pa 880 706}%
\special{pa 878 706}%
\special{pa 876 708}%
\special{pa 874 708}%
\special{pa 872 710}%
\special{pa 868 712}%
\special{pa 864 716}%
\special{pa 862 716}%
\special{pa 860 718}%
\special{pa 858 718}%
\special{pa 856 720}%
\special{pa 854 720}%
\special{pa 846 728}%
\special{pa 844 728}%
\special{pa 842 730}%
\special{pa 838 732}%
\special{pa 834 736}%
\special{pa 830 738}%
\special{pa 822 746}%
\special{pa 820 746}%
\special{pa 816 750}%
\special{pa 810 754}%
\special{pa 804 760}%
\special{pa 802 760}%
\special{pa 760 802}%
\special{pa 760 804}%
\special{pa 754 810}%
\special{pa 750 816}%
\special{pa 746 820}%
\special{pa 746 822}%
\special{pa 738 830}%
\special{pa 736 834}%
\special{pa 732 838}%
\special{pa 730 842}%
\special{pa 728 844}%
\special{pa 728 846}%
\special{pa 720 854}%
\special{pa 720 856}%
\special{pa 718 858}%
\special{pa 718 860}%
\special{pa 716 862}%
\special{pa 716 864}%
\special{pa 712 868}%
\special{pa 710 872}%
\special{pa 708 874}%
\special{pa 708 876}%
\special{pa 706 878}%
\special{pa 704 882}%
\special{pa 704 884}%
\special{pa 700 888}%
\special{pa 700 890}%
\special{pa 698 892}%
\special{pa 698 894}%
\special{pa 696 896}%
\special{pa 688 912}%
\special{pa 688 914}%
\special{pa 686 914}%
\special{pa 686 918}%
\special{pa 684 920}%
\special{pa 684 922}%
\special{pa 682 924}%
\special{pa 682 928}%
\special{pa 680 928}%
\special{pa 680 932}%
\special{pa 678 932}%
\special{pa 678 936}%
\special{pa 676 938}%
\special{pa 676 942}%
\special{pa 674 942}%
\special{pa 674 946}%
\special{pa 672 948}%
\special{pa 672 950}%
\special{pa 670 954}%
\special{pa 670 958}%
\special{pa 668 958}%
\special{pa 668 960}%
\special{pa 662 978}%
\special{pa 662 982}%
\special{pa 660 982}%
\special{pa 660 988}%
\special{pa 658 990}%
\special{pa 658 992}%
\special{pa 656 1000}%
\special{pa 656 1002}%
\special{pa 654 1004}%
\special{pa 654 1012}%
\special{pa 652 1012}%
\special{pa 652 1020}%
\special{pa 650 1022}%
\special{pa 650 1030}%
\special{pa 648 1032}%
\special{pa 648 1036}%
\special{pa 646 1048}%
\special{pa 646 1054}%
\special{pa 644 1056}%
\special{pa 644 1072}%
\special{pa 642 1072}%
\special{pa 642 1098}%
\special{pa 640 1100}%
\special{pa 640 1142}%
\special{pa 642 1142}%
\special{pa 642 1168}%
\special{pa 644 1170}%
\special{pa 644 1186}%
\special{pa 646 1186}%
\special{pa 646 1194}%
\special{pa 648 1204}%
\special{pa 648 1210}%
\special{pa 650 1210}%
\special{pa 650 1220}%
\special{pa 652 1220}%
\special{pa 652 1228}%
\special{pa 654 1230}%
\special{pa 654 1238}%
\special{pa 656 1238}%
\special{pa 656 1242}%
\special{pa 658 1248}%
\special{pa 658 1252}%
\special{pa 660 1252}%
\special{pa 660 1258}%
\special{pa 662 1260}%
\special{pa 662 1264}%
\special{pa 664 1268}%
\special{pa 664 1270}%
\special{pa 666 1274}%
\special{pa 666 1276}%
\special{pa 668 1280}%
\special{pa 668 1282}%
\special{pa 670 1284}%
\special{pa 670 1288}%
\special{pa 672 1290}%
\special{pa 672 1294}%
\special{pa 674 1294}%
\special{pa 674 1298}%
\special{pa 676 1300}%
\special{pa 676 1302}%
\special{pa 678 1306}%
\special{pa 678 1308}%
\special{pa 680 1310}%
\special{pa 680 1312}%
\special{pa 682 1314}%
\special{pa 682 1316}%
\special{pa 686 1324}%
\special{pa 686 1326}%
\special{pa 688 1328}%
\special{pa 688 1330}%
\special{pa 690 1332}%
\special{pa 690 1334}%
\special{pa 692 1336}%
\special{pa 692 1338}%
\special{pa 694 1340}%
\special{pa 694 1342}%
\special{pa 698 1346}%
\special{pa 698 1350}%
\special{pa 700 1350}%
\special{pa 700 1354}%
\special{pa 702 1354}%
\special{pa 702 1356}%
\special{pa 704 1358}%
\special{pa 704 1360}%
\special{pa 708 1364}%
\special{pa 708 1368}%
\special{pa 714 1374}%
\special{pa 714 1376}%
\special{pa 718 1380}%
\special{pa 718 1384}%
\special{pa 722 1388}%
\special{pa 722 1390}%
\special{pa 726 1392}%
\special{pa 726 1394}%
\special{pa 730 1398}%
\special{pa 730 1400}%
\special{pa 732 1402}%
\special{pa 732 1404}%
\special{pa 736 1406}%
\special{pa 736 1408}%
\special{pa 738 1410}%
\special{pa 738 1412}%
\special{pa 742 1414}%
\special{pa 742 1416}%
\special{pa 750 1424}%
\special{pa 750 1426}%
\special{pa 754 1430}%
\special{pa 754 1432}%
\special{pa 770 1448}%
\special{pa 770 1450}%
\special{pa 792 1470}%
\special{pa 802 1480}%
\special{pa 804 1480}%
\special{pa 820 1496}%
\special{pa 822 1496}%
\special{pa 826 1500}%
\special{pa 830 1502}%
\special{pa 834 1506}%
\special{pa 838 1508}%
\special{pa 844 1514}%
\special{pa 846 1514}%
\special{pa 848 1516}%
\special{pa 852 1518}%
\special{pa 854 1520}%
\special{pa 856 1520}%
\special{pa 862 1526}%
\special{pa 864 1526}%
\special{pa 868 1530}%
\special{pa 872 1530}%
\special{pa 878 1536}%
\special{pa 882 1536}%
\special{pa 882 1538}%
\special{pa 884 1538}%
\special{pa 886 1540}%
\special{pa 888 1540}%
\special{pa 890 1542}%
\special{pa 892 1542}%
\special{pa 896 1546}%
\special{pa 900 1546}%
\special{pa 900 1548}%
\special{pa 904 1548}%
\special{pa 904 1550}%
\special{pa 908 1550}%
\special{pa 908 1552}%
\special{pa 912 1552}%
\special{pa 912 1554}%
\special{pa 916 1554}%
\special{pa 918 1556}%
\special{pa 920 1556}%
\special{pa 922 1558}%
\special{pa 924 1558}%
\special{pa 926 1560}%
\special{pa 928 1560}%
\special{pa 932 1562}%
\special{pa 934 1562}%
\special{pa 936 1564}%
\special{pa 938 1564}%
\special{pa 940 1566}%
\special{pa 944 1566}%
\special{pa 944 1568}%
\special{pa 948 1568}%
\special{pa 950 1570}%
\special{pa 954 1570}%
\special{pa 956 1572}%
\special{pa 960 1572}%
\special{pa 960 1574}%
\special{pa 966 1574}%
\special{pa 966 1576}%
\special{pa 972 1576}%
\special{pa 972 1578}%
\special{pa 978 1578}%
\special{pa 978 1580}%
\special{pa 984 1580}%
\special{pa 986 1582}%
\special{pa 992 1582}%
\special{pa 992 1584}%
\special{pa 1000 1584}%
\special{pa 1000 1586}%
\special{pa 1006 1586}%
\special{pa 1008 1588}%
\special{pa 1016 1588}%
\special{pa 1016 1590}%
\special{pa 1024 1590}%
\special{pa 1026 1592}%
\special{pa 1036 1592}%
\special{pa 1036 1594}%
\special{pa 1048 1594}%
\special{pa 1048 1596}%
\special{pa 1062 1596}%
\special{pa 1064 1598}%
\special{pa 1082 1598}%
\special{pa 1084 1600}%
\special{pa 1158 1600}%
\special{pa 1158 1598}%
\special{pa 1178 1598}%
\special{pa 1178 1596}%
\special{pa 1192 1596}%
\special{pa 1194 1594}%
\special{pa 1204 1594}%
\special{pa 1206 1592}%
\special{pa 1216 1592}%
\special{pa 1216 1590}%
\special{pa 1224 1590}%
\special{pa 1226 1588}%
\special{pa 1234 1588}%
\special{pa 1234 1586}%
\special{pa 1240 1586}%
\special{pa 1242 1584}%
\special{pa 1248 1584}%
\special{pa 1250 1582}%
\special{pa 1256 1582}%
\special{pa 1256 1580}%
\special{pa 1262 1580}%
\special{pa 1264 1578}%
\special{pa 1268 1578}%
\special{pa 1270 1576}%
\special{pa 1274 1576}%
\special{pa 1276 1574}%
\special{pa 1280 1574}%
\special{pa 1282 1572}%
\special{pa 1284 1572}%
\special{pa 1288 1570}%
\special{pa 1292 1570}%
\special{pa 1292 1568}%
\special{pa 1296 1568}%
\special{pa 1298 1566}%
\special{pa 1302 1566}%
\special{pa 1302 1564}%
\special{pa 1306 1564}%
\special{pa 1306 1562}%
\special{pa 1310 1562}%
\special{pa 1312 1560}%
\special{pa 1316 1560}%
\special{pa 1316 1558}%
\special{pa 1320 1558}%
\special{pa 1320 1556}%
\special{pa 1324 1556}%
\special{pa 1324 1554}%
\special{pa 1328 1554}%
\special{pa 1330 1552}%
\special{pa 1332 1552}%
\special{pa 1334 1550}%
\special{pa 1336 1550}%
\special{pa 1338 1548}%
\special{pa 1340 1548}%
\special{pa 1342 1546}%
\special{pa 1344 1546}%
\special{pa 1346 1544}%
\special{pa 1354 1540}%
\special{pa 1356 1540}%
\special{pa 1360 1536}%
\special{pa 1362 1536}%
\special{pa 1364 1534}%
\special{pa 1368 1532}%
\special{pa 1370 1530}%
\special{pa 1372 1530}%
\special{pa 1374 1528}%
\special{pa 1376 1528}%
\special{pa 1380 1524}%
\special{pa 1384 1522}%
\special{pa 1388 1518}%
\special{pa 1390 1518}%
\special{pa 1392 1516}%
\special{pa 1394 1516}%
\special{pa 1398 1512}%
\special{pa 1400 1512}%
\special{pa 1402 1508}%
\special{pa 1404 1508}%
\special{pa 1406 1506}%
\special{pa 1408 1506}%
\special{pa 1410 1502}%
\special{pa 1412 1502}%
\special{pa 1414 1500}%
\special{pa 1416 1500}%
\special{pa 1424 1492}%
\special{pa 1426 1492}%
\special{pa 1430 1486}%
\special{pa 1432 1486}%
\special{pa 1448 1470}%
\special{pa 1450 1470}%
\special{pa 1470 1450}%
\special{pa 1470 1448}%
\special{pa 1486 1432}%
\special{pa 1486 1430}%
\special{pa 1492 1426}%
\special{pa 1492 1424}%
\special{pa 1500 1416}%
\special{pa 1500 1414}%
\special{fp}%
}}%
% LINE 2 0 3 0 Black White
% 4 1120 1120 1360 1600 1120 1120 1480 1600
%
{\color[named]{Black}{%
\special{pn 8}%
\special{pa 1120 1120}%
\special{pa 1360 1600}%
\special{fp}%
\special{pa 1120 1120}%
\special{pa 1480 1600}%
\special{fp}%
}}%
% CIRCLE 2 0 3 0 Black White
% 4 1120 1120 1198 1324 1708 2290 1960 2248
%
{\color[named]{Black}{%
\special{pn 8}%
\special{ar 1120 1120 218 218 0.9307082 1.1050995}%
}}%
% STR 2 0 3 0 Black White
% 4 1496 1682 1496 1742 2 0 0 0
% ${\rm A}_k$
\put(14.9600,-17.4200){\makebox(0,0)[lb]{${\rm A}_k$}}%
% STR 2 0 3 0 Black White
% 4 1204 1686 1204 1746 2 0 0 0
% ${\rm A}_{k-1}$
\put(12.0400,-17.4600){\makebox(0,0)[lb]{${\rm A}_{k-1}$}}%
% STR 2 0 3 0 Black White
% 4 1014 1120 1014 1180 2 0 0 0
% C
\put(10.1400,-11.8000){\makebox(0,0)[lb]{C}}%
\end{picture}}%
\end{center}
}
%--------------------------------------------------------------
\end{framed}
%\end{FRAME}
%--- 解答 ------------------------------------------------------------------------
{\footnotesize
}% footnotesize
%%%%%%% ■ 本文終了 ■ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
Copyright(c) 2020 Infonic Co., Ltd. All rights reserved.