DERIVE for Windows version 5.05 DfW file saved on 11 Nov 2002 f(x):=(3·x^2 + 7·x - 9)/(x + 1) f1(x):=(3·x^7 + 4·x^6 + 3·x)/(2·x^7 + 9) f2(x):=(3·x^7 + 4·x^6 + 3·x)/(x^6 + 5·x) f3(x):=(8·x^9 + 16·x^8 + 5)/(2·x^8 + 4·x^2) f4(x):=(2·x^6 + 3·x^4 + 7)/(x^5 + x^3 + x) f5(x):=(4·x^4 + 5·x^3 + 8)/(9·x^5 - 7·x^3 + 2·x) f6(x):=(8·x^4 + 4·x^3 + 9)/(2·x^3 + 1) f7(x):=(3·x^9 + 6·x^8 + 3)/(x^8 + 3·x^7) ÿÿCTextObj ÙMÿ {\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\f0\fs32 Skr\'e5 asymptoter. \par \b0\fs24 \par \b\fs28 A.\b0\fs24 Tegn grafen for funktionen f: \par } ÿÿCExpnObj8Yø‰Userð¿f(x):=(3*x^2+7*x-9)/(x+1)€•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 Tegn ogs\'e5 linien med ligningen y = 3x+4. Denne ligning kaldes en skr\'e5 asymptote til grafen for f. \par } €ÇÙÿ\{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\f0\fs28 B\b0\fs24 . Omskriv forskriften for f v.hj.a. "Simplify" og "Expand" \par Giv en definition p\'e5, at linien med ligning y = ax + b er skr\'e5 asymptote til grafen for f. \par } €Ù8ÿL{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\f0\fs28 C.\b0\fs24 Tegn graferne for nedenst\'e5ende funktioner, og bestem, hvilke af graferne der har en skr\'e5 asymptote. Bestem en ligning for denne asymptote. \par } €8D€Userð¿"f1(x):=(3*x^7+4*x^6+3*x)/(2*x^7+9)€8ŒÈUserð¿"f2(x):=(3*x^7+4*x^6+3*x)/(x^6+5*x)€8ÔUserð¿%f3(x):=(8*x^9+16*x^8+5)/(2*x^8+4*x^2)€8XUserð¿"f4(x):=(2*x^6+3*x^4+7)/(x^5+x^3+x)€8d Userð¿(f5(x):=(4*x^4+5*x^3+8)/(9*x^5-7*x^3+2*x)€¬ÙÕÿ&{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\f0\fs28 D\b0\fs24 . Opstil en generel regel for, hvorn\'e5r en polynomiumsbr\'f8k har en skr\'e5 asymptote. Bevis denne regel. \par } €áÙ ÿ5{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\f0\fs28 E\b0\fs24 . Bestem ved h\'e5ndkraft (uden brug af Derive) en ligning for de skr\'e5 asymptoter til grafen for f\'f8lgende funktioner: \par } €8RUserð¿ f6(x):=(8*x^4+4*x^3+9)/(2*x^3+1)€8^šUserð¿"f7(x):=(3*x^9+6*x^8+3)/(x^8+3*x^7)€¦Ù¹ë{\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 Kontroll\'e9r v. hj.a. Derive, at disse ligninger er rigtige. \par } ÿÿÿð