DERIVE for Windows version 5.05 DfW file saved on 07 Nov 2002 f(x):=(2x^4 - 9)/(x^4 + x^3) f1(x):=(x^7 - 5x)/(x^6 - 3x + 4) f10(x):=(1/2)^x + 2 f11(x):=(38/25)^(4 - x) f12(x):=2^x/x^14 f13(x):=(x^3 - 7)/(1/2)^x f2(x):=(x^3 + x^2 - 9x)/(x^4 + 7x) f3(x):=(x^12 - x^9)/(3x^12 + 4x) f4(x):=(4x^9 + 5x^3)/(2x^7 + 4x^5) f5(x):=(x^3 - x^2 + x - 5)/(x^8 - x^3 - 9) f6(x):=(x^6 - 8x^5 - 9x^2 + 3)/(x^2 - x + 7) f7(x):=(x^3 - 2x^5 + 6x - 1)/(x^5 + x^4 - 4) f8(x):=(x^3 - 2x^2 + x^5 - 10)/(x^3 + 4x - 3x^6) f9(x):=7^x CTextObj M {\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\f0\fs32 Vandrette asymptoter.\b0\fs24 \par \par \b\fs28 A\b0\fs24 . Tegn grafen for funktionen f: \par } CExpnObj8YUserf(x):=(2*x^4-9)/(x^4+x^3){\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs24 og tegn linien med ligning y=2. Denne linie kaldes en vandret asymptote til grafen for f. \par } {\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 Opskriv definitionen p\'e5, at linien med ligning y = a er vandret asymptote til grafen for f. \par } 1L{\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 vandret asymptote. Skriv en ligning for disse asymptoter. \par } 8=yUserf1(x):=(x^7-5*x)/(x^6-3*x+4)8Userf2(x):=(x^3+x^2-9*x)/(x^4+7*x)8 Userf3(x):=(x^12-x^9)/(3*x^12+4*x)8QUser"f4(x):=(4*x^9+5*x^3)/(2*x^7+4*x^5)]0{\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 Skriv en generel regel for, hvorn\'e5r grafen for en polynomiumsbr\'f8k har en vandret asymptote. Bevis denne regel. \par } L{\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 (uden at tegne grafen), for hvilke af nedenst\'e5ende funktioner grafen har en vandret asymptote. Bestem en ligning for disse asymptoter. \par } 8User f5(x):=(x^3-x^2+x-5)/(x^8-x^3-9)80KUser$f6(x):=(x^6-8*x^5-9*x^2+3)/(x^2-x+7)8W(User$f7(x):=(x^3-2*x^5+6*x-1)/(x^5+x^4-4)8(User )f8(x):=(x^3-2*x^2+x^5-10)/(x^3+4*x-3*x^6){\rtf1\ansi\ansicpg1252\deff0\deflang1030{\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\b\f0\fs28 F\b0\fs24 . Bestem de vandrette asymptoter til graferne for f\'f8lgende funktioner: \par } 8 !User  f9(x):=7^x8-EUser f10(x):=(0.5)^x+28QiUser f11(x):=(1.52)^(-x+4)8uUser f12(x):=2^x/x^148Userf13(x):=(x^3-7)/(0.5)^x