MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C67B7F.2D41AE20" このドキュメントは単一ファイル Web ページ (Web アーカイブ ファイル) です。お使いのブラウザ、またはエディタは Web アーカイブ ファイルをサポートしていません。Microsoft Internet Explorer など、Web アーカイブをサポートするブラウザをダウンロードしてください。 ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う

このプレゼンテーシ= ョンの内容は、お使= 2356;のブラウザで正しӔ= 7;表示されない可能性&= #12364;あります。 このプレゼンテーシ= 2519;ンは、より新しいӡ= 6;ージョンの Microsoft Internet Explorer 用に最適化されてい= 2414;す。

続行する場合は、次= をクリックしてくだ= 2373;い : ここ.

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マスタ = 2479;イトルの書式設定
マスタ テキスト{= 98;書式設定
2 レベル <= /div>
3 レベル <= /div>
4 レベル <= /div>
5 レベル
<日付/時&#= 21051;>
<フッター>
<#>
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<ヘッダ= ;ー>
<日付/時&#= 21051;>
<フッタ= ;ー>
<#>
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
方程式を#= 299;いてみよう
&#= 38745;岡理工科大学
&#= 29702;工学部 情報シス|= 86;ム学科
&#= 24184;谷智紀(こうや {= 92;ものり)
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
概要
&= #12467;ンピュータのしく = 415;
&= #34920;計算ソフトとは?
方程式&= #12399;なぜ必要&= #12363;?
方程式を解く方= 7861;
グラフを使う方法
中点法
レギュラ・ファ= 2523;シ法
&= #35506;題 <= /div>
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&= #12467;ンピュータのしく = 415;(1/2)<= /div>
ä= 10;くの処理()はここで行= われる
データを蓄&#= 12360;る場所
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コンピュ = 540;タのしくみ(2/2)
2進回路の = 068;み合わ= &#= 12379; → 単純な計算ӕ= 5;&#= 12363;出来ない &#= 22235;則演算の組み合わ= &#= 12379;で全てを表現する = &#= 20294;し,沢山繰り返し{= 90;= &#= 12418;良い(一回辺りのš= 36;&#= 31639;時間はとても小さ{= 56;= &#= 12363;ら)
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(1) データ入力
(2) データ処理
(3)データ出力
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&= #34920;計算ソフトとは?(1/3)<= /div>
&= #20363;えばExcel(= エクセル)が有名。
&= #12475;ル(cell)= にデータӛ= 4;入力し,計算したり&= #12464;ラフを= 描いたりӗ= 1;きる。 一つのフӜ= 9;イルに複数のシート<= /span>()を作ることができる。 <= /div>
B3セル
グラフ|= 54;ィザード
シート名
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Content-Type: image/gif R0lGODlhRwAOAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgBD AAkAgAAAAP8AAAI5hI+py+0Xnpy0goCt3hN7DoaGR45Rhp7qtaLje8FRTM82iafsrvenDKwFb7mZ 6CjJIZfJD/PZyCgKADs= ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0030.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
&= #34920;計算ソフトとは?(2/3)<= /div>
計算は,半= ;角の「=3D&#= 12301;に続いて計算式をÐ= 37;力。
計算= ;式・・・セルの指定&#= 12392;加減乗除(+, -, *= , / ), = 累乗(^)・・= ;・等の組み合わせで&#= 34920;現する。
[肩慣らし]
A列:1~5まで入力
B列:A列の値の2乗を自動<= span style=3D'position:absolute;top:20.08%;left:32.8%;width:57.14%;height:7.94%= '>計算
C列:A列とB列の相加平均を自動計算
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表計= ;算ソフトとは?(3/3)
[計算方法]
A列に1から= ;5&#= 12414;での自然数を入力z= 90;
B1= A1&#= 12398;2乗を計算→「=3DA1^2&#= 12301;
C1= A1&#= 12392;B1&#= 12398;値の相加平均を計ļ= 39;→=3D(A1 + B1) / 2」。
B1, C1を選= ;択し,右下の黒ポッ&#= 12481;をドラッグして5行分= ;コピーする。
•<= /span>
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0003.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
方程式はなぜ必要か?(1/2)
問題「直角ӛ= 4;なす一辺の長さが1メートルの,直= 5282;二等辺三角形の= 6012;辺の長さは何メーӠ= 8;ルか?」
   メートル= 5292;では実用上困る。 <= /span>
小数で表現する= 2392;?
(電卓を使うとよ= 2356;) =
何故分かるか?= 3;
= =
1
1
x
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方程= ;式はなぜ必要か?(2/2) 
ピタゴラスの定= 702;と方程式
  斜辺の長さ x メーӠ= 8;ルとすれば
  より
&= #12288; この方程式を x につӓ= 6;て解き,そのઽ= 1;の解を求めればよい。
 &= #12288;以下では,全て= 2398;方程式を f (x) =3D 0 と表ங= 4;する。    ӌ= 8;
  上記の方程式も= 3;
  と変形して扱う= 2290;
•<= /span> <= /div>
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0004_image030.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjB4wMbAxMgJYn2IYmQAMpgdGRkYmBhkwLKsQMzJBGMxMTJCWYxM//// B7P0GCWgYtxwdTxMDEwP2ISALDU2fgYphv8gxQwCQP4BIGs7EC9gY2DYDjSMG6qGh8E3sSQjpLIg lYHBAGz3byaF/xAXTgBZysDCxCAQkpmbWqzgl1quEJSfm5jH8OCJDsMb65ZaBYb22krhtIssQHW6 QNUcQNqI6wuDJhtIq1EljL+RGZXPzwjhQ+xr+EeefYwMIPoD3N4FjBWsICMMK2F8BmYIH4s9TCB7 gitzk/JzGBiO8nF9AZmNy18Qexjh9nSwgIzQhtvzD+wfWwx7GCn0jw8DyISKSi5obHGBYxQcTNC4 EgKrhfqpgZGJiSm4srgkNZfhIshcBqAORYYuiAYg+PNMhwHdT8xgGQA9f5WAmAIAAA== ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0004_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhcAAhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABgBl ABUAgwAAAAAAAAwKCwoICQcGBwMDAwYFBQUEBAsKCgkHCAcGBggHBwkICAsJCgECAwECAwTVEMhJ a7g1680t7mAoXYE4TqWpbinQrmr7mjNsn7ddh3se+7BeRwgEEYuWILIiGBAKnKOq+WTplhSD4aOR mrTc5Mp7C1PIsR0at6apcUaR2QU3ktry2t3Ln+0lVAcIEgMFBlh2SH08JAQAAxeHiFF4GYsiCRcC CgI6e5+UinkqBwGSk4lFlyILAQyojJ6ff5ZoDQEKsKlAqyGtlbzAZ6MiDQ1bDWWzd6GqxCGvmQwC C7pdwijPGloCCRK3BguD1hS3Acm8IeboGgoB3hMHguRntDlHoBoRADs= ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0004_image032.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBQYGFgYuQEsQwiGBmADGZFRgYGJgYZsCwrEHMywVhMjIxQFiPT//// wSw9RgmoGDdcHQ8TA5MCixCQpcbGzyDF8B+kmEEAyD8AZG0H4gfMDAzbgYZxQ9XwMPgmlmSEVBak At0Btvs3U8M/iAsngCxlYGFiEAjJzE0tVvBLLVcIys9NzGN48ESH4Y11S60CQ3utkVDafBagOl2g ag4gbcS1gFGLGaTVqBJinsJ/8sxjZADRH+DmfmHgZ0Q2F8WdTCBzgytzk/JzGBiaRbhKQWbhcifE XEa4e/+BzbXFMJeRIvcuYPRhAJlQUckFDW0ucIyAgwEa1kJgtVA/NDAyMTEFVxaXpOYyzAeZywDU ocjQBdEABH+e6TCg+4EZLAMA7e+3EVgCAAA= ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0004_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhQQAgAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABgA4 ABQAgwAAAAAAAAkICAUEBAMDAwgHBwwKCwsKCgsJCgoICQYFBQcGBwkHCAcGBgECAwECAwShEMhJ abg16827DhPojWRpmWj6qawqtrD3xpkwBERhuLRWXEDCATXrSRAEhCRBCChMoiJtMZwgMCQg1ghg ZAKDyYExSCwJT27JEBCELuHEJa0eMSvyQEKxS2n/QCQDShUKAQ11KAJeGXILiSUHBRtXBJAjBowa DIZVfoB/HWYUhABuPwkGk5eNFQUKCgIJSnINC6WsEoaAe0kTA4O5FLuABhEAOx== ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0004_image034.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBwYGNgYuQEsQKiGBmADGZDRgYGJgYZsCwrEHMywVhMjIxQFiPT//// wSw9RgmoGDdcHQ8TA5MDmxCQpcbGzyDF8B+kmEEAyD8AZG0H8dgYGLYDDeOGquFh8E0syQipLEhl YDAA2/2bqeEfxIUTQJYysDAxCIRk5qYWK/illisE5ecm5jHc+ajD8Ma6pVaBob1WmD9tIgtQnS5Q NQeQNuJawGjCCtJqUAnj/2IC8Y0qIeYr/CfPfEYGEP0Bbs8XBn5GZHNR3M0EMje4MjcpP4eBYbkE 1x6QWbjcDTGXEe5+PhaQEbZw9z8D26OLYQ8jRe5fwOjDADKhopILGhtc4BgDBws0LoTAaqF+amBk YmIKriwuSc1lmAgylwGoQ5GhC6IBCH581mFA9xMzWAYAuK8n53gCAAA= ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0004_image035.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhYAAfAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABgBV ABMAgwAAAAAAAAkICAUEBAMDAwgHBwwKCwsKCgYFBQsJCgoICQcGBgcGBwkHCAECAwECAwTmEMhJ Z7g16827/2BggWRpnpyIrmxbqW4sf/AsDAFRGPN0IIFB4lSLFS5IwqF3CCgAisCQVHQlCFMFIYDo DRaTwoAqqa4Yy0kCI4s+JW4a0oxqZIKz4xTQZEgODQNvWl09HQYBAjNAPBZjAEhjUVyGHVo9bBYw kwoIjZUcQhtzpEh3RZkAQGCgHQJ2mKg1UX5EpaQcBwWVOC+FEmsErRsGsIYMUmoBtRINQGnDFG9q p7emFXFwThOKRwoGu9FQFQW/Ll8TDGMIAgpDUQsMe61ApdNW21FDCFgTA6LR6pX6FCMBjgVTIgAA Ow== ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
方程式を#= 299;く方法
グラフ= ;を使う方法
中点法= ;
レギュ= ;ラ・ファルシ法
(ニュート = 531;法)
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0006.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
グラӢ= 1;を使う方法(1/3)<= /div>
&#= 26041;程式の解 x f (= x) =3D 0 とな= ;る
<= span style=3D'mso-spacerun:yes'>  y = =3D f (x) = &#= 12398;グラフを書いて,x &#= 36600;と交点の x &#= 24231;標を求めればよ = 356;。
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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhNQBOAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAGQAW ADMAgAAAAP8AAAJghI+poe3sooEy0touRnqf7gXgNpLecqIpt36t+4ovUGK1dOMzPecsHJLJTqKi 72M0BpNH5pGWTEWlw1XVGlMGE9dM6Wt7mLhEcsg8nkjR4V9afXZXQL7RrWbPFSddW64AADs= ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0018.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
グラ= ;フを使う方法(2/3)
=  [長所] グラフが簡単に描Ӕ= 9;れば,どの辺に解が= あるかを予め知= 2427;ことが出来る。
Excel&= #12398;グラフ機能を活用 = 377;る。
手順:
<= span style=3D'font-size:86%;mso-fareast-hint:yes'>1.A列に x &= #12398;値を一定刻みで並 = 409;る
<= span style=3D'font-size:86%'>2.B列に f (x)の値を自ࡈ= 5;的に計算させて並べ&= #12427;
3.計算したA, B列のセルӛ= 4;選択し,グラフウィ&= #12470;ードを起動してӞ= 4;ラフを描く。 <= /div>
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0019.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
&= #12464;ラフを使う方法(3/3)<= /div>
[短所= ;] 正確な交点= ;の位置を求めるのは&#= 25163;間がかかる。
<= span style=3D'visibility:hidden'>
=
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R0lGODlhkgA0AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQCO ADIAgAAAAAAAAALQhI+py+0Po5wxWIqz3rwrCwaHSALlaaboqrbs68WyEdbzjedebeu36At+TLyL 8IjcsEa9VJIDfGJQkJD0mgS1psYRNhPFUmPhr3m6lZbPjvXOxY6L0/KEu464L5b4vm7sN6HXFwUY eDhTgpi4mNf4CPk4iDcZaXmZFVmJydnJCLnpKTpKEcpmSpqqaqe56vr6gGomC1t7STtnq/uKe9W7 C0zYGkzs+ft0XKzsO7zs3JiMFP1MnTMtdF2t/Qa67R2X7RP+TV7RTAyTDqfOTkdcAAA7 ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0007.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
練習1
y =3D x2 - 2の&= #12464;ラフを描き,方ఴ= 3;式 x2  2 =3D 0 解がどの๟= 4;りにあるかを確認せ&= #12424;。但し,全ての解がどの辺に= 2354;るのか分かる範囲ӗ= 5;設定す= ること
1. xの範囲が-10から10まで,刻み幅1
2. -5から5まで,&= #21051;み幅0.5
3. -2から2まで,&= #21051;み幅0.1
4. 1&= #12363;ら2まで,刻ә= 5;幅0.05
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0021.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
&= #12464;ラフの描き方(1/2)<= /div>
1.&= #26368;初のxの値を代ࠣ= 7;し,yの値を自ࡈ= 5;計算させӚ= 7;。
2.
2.&= #27425;のxの値を,࠹= 1;み幅を加えて自動計算させᦁ= 2;yの値は上ӗ= 8;計算式をコピーしてӕ= 1;れも自動計算させる&= #12290;
3.
3.
3.
3.&= #26368;後のxの値になӚ= 7;までA, B列のセ= ルを下にӞ= 7;ピーし続ける。 <= /div>
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&= #12464;ラフの描き方(2/2)<= /div>
4.計算が完了= ;したら,計算したセ&#= 12523;を全て選択し,グラ = 501;ウィザードを起動し= ;て「散布図」を選ぶ = 290;
5.グラフを描= ;く。
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N7bW9xapFKsO2dQCxUdR7c1X+03H/PeT/vs077Zdf8/M3/fw0AP1dX/tOb94f4ew/uiiue1K6uDf yk3Ep6fxn0FFAH//2X== ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0008.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
中点法(1/2)
1.&#= 26041;程式の解 x &#= 12364;一つだけ含まれるÕ= 06;間[a, b]<= /span>&#= 12434;決める。
2. c = =3D (a + b) = / 2 として区間= の中点を設定 = 375;, [a, c](= &#= 24038;), [c, b](&#= 20596;)どちら= ;かの,解&#= 12364;含まれている区間|= 34;見つける
3.解が= ;含まれている区間を&#= 26032;たに[a, b]<= /span>&#= 12377;る。
4.1&#= 65374;3の手続= ;きを続ける。
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0009.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
&= #20013;点法(2/2)<= /div>
[原理] 解が一つ = 384;け区間[a, = b]
に含まれている = ;
 → f (= a) f (= b) < 0
区間の&#= 20013;点をc =3D (a += b) / 2とすると = ;
(1= ) [a, c]<= /span>&#= 12395;解が含まれている f (a) f (= c) < 0
<= span style=3D'mso-tab-count:1;width:4.07%'> (2) [c, b]<= /span>&#= 12395;解が含まれている f (c) f (= b) < 0
のどちらか= ;になる。よって
(1= )&#= 12398;場合は,b :=3D c, aはそのまま= ;
(2= )&#= 12398;場合は,a :=3D c, bはそのまま= ;
としてこの手続 = 365;を繰り返す。
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ExcelIF関数= ;
=3DIF(
条件式,
条件式が満たされ{= 90;いる時の値()
条件式がଌ= 8;たされていない時の&= #20516;()
) =
次のaの値・・ӥ= 9; =3DIF( f <= /i>(a) * f <= /i>(c) < 0, a, c) =
次のbの値・&= #12539;・ =3DIF( f <= /i>(c) * f <= /i>(b) < 0, b, c)
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
練習2
練習= 1の結果= ;を使って,a, bを設定し,中点&#= 27861;を用いて方程式 x2  2 =3D 0= &#= 27491;の解を見&#= 12388;けてみよ。
------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
Excelで中点法を= ;実行する(1/3)
1.方程式と見= ;出しを記入し,最初&#= 12398;a, b値をセルに記= 837;する。
2. c, f (a), f (b), f (c)の値= ;を自動計算させる。
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t8gxtH9a8kP/ACKU/wD2BIv/AEFq6qHt/uLQB2nkxf3BR5MX9wVx9FAHYeTF/cFHkxf3BXH0UAdh 5MX9wVTs9Q03ULy8tLWRZZbFxHcAA4RiM4z34rm65XwX/wAf2t/9fX9WoA9JGsaQdU/s0Sj7RuKD 5G2lwNxTdjG7HOM5p1lqmnahcNDbJK+xmUv5DhMqcMNxGDggjrXmSfftf+w/L/6DJW5of/ILX/rr L/6MagDsLuKPyofkHQ0Vydx/q4vxooA//9k= ------=_NextPart_01C67B7F.2D41AE20 Content-Location: file:///C:/24F9C636/equation2006.files/slide0024.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 方程式を解いてみ = 424;う
Excelで中点法ӛ= 4;実行する(2/3)<= /div>
3.(1)の判定をӕ= 7;るための数式を記入&= #12377;る。
4.
4.
4.
4.
4.(2)の判定をӕ= 7;るための数式を記入&= #12377;る。
5.
5.
5.
5. cから f (c)&= #12414;では上の式をその = 414;まコピーする。 <= /div>
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