DERIVE for Windows version 5.05 DfW file saved on 12 Nov 2002 g(x):=(x^2 - x - 2)/(x + 1) hCross:=APPROX(56451612903225801/100000000000000000) vCross:=APPROX(4017857142857143/5000000000000000) ÿÿCTextObj Ù$Ö{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\f0\fs32 Gr\'e6nsev\'e6rdier i DERIVE.\b0\fs24 \par } €0ÙCÝ{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Indtast en funktion, f.eks som nedenst\'e5ende: \par } ÿÿCExpnObj8OhgUserð¿x^2+4€sÙ™ÿ{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Klik derefter p\'e5 lim i \'f8verste bj\'e6lke, og v\'e6lg "Simplify" \par Hvad er konklusionen? \par } €¥Ù¸ÿ*{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Pr\'f8v ogs\'e5 med nedenst\'e5ende funktion, marker kun g(x) og v\'e6lg s\'e5 "lim" kun p\'e5 den - ikke selve forskriften. \par } €8ÄØôUserð¿g(x):=(x^2-x-2)/(x+1)€Ù»{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Find ogs\'e5: \par } €8x7 Lim(#2',x)ð¿LIM(g(x),x,2,0)€8C€[ Lim(#2',x)ð¿LIM(g(x),x,-1,0)€gÙ ÿ{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Beregn g(2) og g(-1). \par Er du tilfreds med resultatet?? \par Tegn grafen for g og sammenlign. \par } €¬Ù¿Ø{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Beregn nu f\'f8lgende gr\'e6nsev\'e6rdier: \par } €8ËÈ Lim(User,x)ð¿LIM((x^2-4*x+4)/(x^2-4),x,2,0)€8ÐO Lim(User,x)ð¿LIM((x^2-4*x+4)/(x^2-4),x,-2,0)€8[Ø— Lim(User,x)ð¿LIM((x^2-4*x+4)/(x^2-4),x,-2,1)€8£Øß Lim(User,x)ð¿ LIM((x^2-4*x+4)/(x^2-4),x,-2,-1)€ëÙþÖ{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Sammenlign med en graf over funktionen. \par } € Ùÿ{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}{\f1\fnil\fcharset2 DfW5 Printer;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Bestem ogs\'e5 f\'f8lgende gr\'e6nsev\'e6rdier. \f1\'96\f0 skrives "inf". \par } €8)Èe Lim(#5',x)ð¿  LIM((x^2-4*x+4)/(x^2-4),x,inf,0)€8qЭ Lim(#9',x)ð¿ !LIM((x^2-4*x+4)/(x^2-4),x,-inf,0)€8¹ØéUserð¿ g(x):=(x^2-x-2)/(x+1)€8õ€  Lim(#11',x)ð¿ LIM(g(x),x,-2,0)€%Simp(Lim(#11',x)){®Gáz¤? -4€81X=Userð¿g(2)€IU Simp(#14'){®Gáz„?0€8a`mUserð¿g(-1)€y… Simp(#16)?€8‘ØÍUserð¿LIM((x^2-4*x+4)/(x^2-4),x,-2,1)€Ùå Simp(#18){®Gáz„?-inf€8ñØ-Userð¿ LIM((x^2-4*x+4)/(x^2-4),x,-2,-1)€9E Simp(#20){®Gáz„?infÿÿÿð