**TI82** Grouped file dated 07/26/93, 08:344_DEMO>0??4? DEMO_AAINI?_POLINILF?1P?3\1+1?0\1+1?3\1+2?0\1+3?1\1+4?_POL1??1>_POLSGNSP?u??*STUDY)OF*?*PXjX3q3X?_SP1?*P1*?1I?3J?_POLDERSP?3>_POLAFF?3>_POLSGNSP?]3A?8B?*^*^??_POLTABV =FRAFF=;?*PXj?11C?1>_SPAFP0?_SP1?*QXj?11C?2>_SPAFP0?_SP1 XFRASYMPTXV?*ASYMPTOTIC)FUNC*?1+7 >_POLCOP?2+10 >_POLCOP?_POLDSP??*Yj?14C?8>_SPAFP0?_SP1S GFRDEFGE1P??*DEF:)P*?_SP1?_POLSAI?_POL1?2P??*DEF:)Q*?_SP1?_POLSAI?_POL2 yFRDERyw1I?3J?_POLDERSP?2I?4J?_POLDERSP?3I?2J?5K?_POLMUL?1I?4J?6K?_POLMUL?5I?6J?3K?_POLDIF??*PQqPQj*?3>_POLAFF FRDF*DOMAIN)OF*?*FUNCTION*??1;12+1;12 ]?2+4 >_POLCOP?2P??*SOLVING*?_POLR?]?]]?ε]j2??*DjR*??*DjR)q?I+2+]q1?]I?I+1+*X*?I+2+Iq1??? FRETUDE_FRDF?_SP1?_POLINILF?_FRSIMPL1??*FX*?_FRDER??*ROOTS)OF)F?3+4 >_POLCOP?_POLR??*SIGN)OF)F?_POLT1?3>_POLT2?2+11 >_POLCOP>2\11+2?11>_POLT2?_FRTQUO?_POLTABS?*^^*^??_POLTABV?_FRASYMPT FRMENU1P?*^^*^?_POLINILF?A?u??*PXQX*+*DEF)P+)Q*+1+*SIGN*+2+*DERIVE*+3+*SIMPLIFY*+4+*VALUE*+5+*STUDY*+6+*EXIT*+7??1>_FRDEF>A?2>_FRSGN>A?3>_FRDER>A?4>_FRSIMPL2>A?5>_FRVAL>A?6>_FRETUDE>A??7> FRSGN_POLINILF?1;12+1;12 ]?1+4 >_POLCOP?1>_POLMSG1?1P?_POLAFF?_POLR?_POLFACTO??_POLINILF?2P?_POLMSG1?2>_POLAFF?2+4 >_POLCOP?_POLR?_POLFACTO????_POLT1?1>_POLT2?2>_POLT2?_FRTQUO?_POLTABS FRSIMPL1?*SIMPLIFICATION?I+2+]?]IA?β^Ak1;10??^A+8j0@^A+8j0?A+^A+^A?1>_POLFACT1?_POL1?2>_POLFACT1?_POL2?_FRAFF??? FRSIMPL2u??*PGCDP+Q?1+7 >_POLCOP?2+10 >_POLCOP?_POLPGCD?10>_POLAFF?\10+1k1??*CANNOT*?*SIMPLIFY*?_SP1???*PPGCDP+Q?10+5 >_POLCOP?1+7 >_POLCOP?_POLDSP?8>_POLAFF?8+1 >_POLCOP??*QPGCDP+Q?2+7 >_POLCOP?5+10 >_POLCOP?_POLDSP?8>_POLAFF?8+2 >_POLCOP FRTQUO\?r2A?L+A \?100\L+1?4\L+A?K+2+Aq1+2?\1+K\2+Kl0??1\L+K??1\L+K???K+3+Aq2+2?\2+K+8o0??0\L+K??3\L+K???Lp1L FRVAL ?X?^ NPOL1NL\1+1n1??*#\1+IXIq1+I+2+\1+1p1+1p\1+1*^??*\1+1*^? NPOL2NL\2+1n1??*#\2+IXIq1+I+2+\2+1p1+1p\2+1*^??*\2+1*^? NPOL3NL\3+1n1??*#\3+IXIq1+I+2+\3+1p1+1p\3+1*^??*\3+1*^? POLAFFrX?0C?X?_SPAFP0?_SP1 hPOLAJOUThf*Xj?rX?X?_SP1?βXl]??0J?I+2+]q1?β]IqXk1;08?1J??Jj0??1p]]?X]r?]?? POLCHSEV?*OBVIOUS)SOLUT:*?10A?*#\4+IXIq1+I+2+\4+1p1+1p\4+1*^?2+2+1+1 c*?J+1+4?c*JX?^X+8j0>XA??Aj10??*NO)OBVIOUS)SOL:*????? POLCHSOL\4+4A?\4+3I?\4+2J?\4+1K?*AX3pIX pJXpK*^????t??1c ?1c ?~ ??*CONSTRUCTION)?*OF)P::::?2+5+P?0?^??*MOVE)CURSOR)TO*?*INTERSECT:)POINT*??"^+X+XA?u LPOLCHXLJA?*CHOOSE)POLY*+*P1*+1+*P2*+2+*P3*+3?1>1P>B?2>2P>B?3>3P>B?B> POLCLRrX?1\X+1?0+\+X\ POLCOPr]?\?r2Y?X+1+Y?\]1+X\]2+X???\]1+1\]2+1?]2l3??]2j1>_POL1?]2j2>_POL2?]2j3>_POL3 POLDEF*DEF)POLY*+*DEF)P1*+C+*DEF)P2*+D+*DEV)^)ql)P1*+A+*DEV)^)ql)P2*+B+*EXIT*+E?A?*^*^?1>_POLDEV??B?*^*^?2>_POLDEV??C?1>_POLSAI?_POL1??D?2>_POLSAI?_POL2??E? APOLDERA?_POLCHX??PI?10J?_POLDERSP?*P:*?1+2+P?10>_POLAFF?_POLMEMO NPOLDERSPNLJ>_POLCLR?\I+1m0??L+1+\I+1?L\I+Lp1\J+L??\I+1q1\J+1 PPOLDEVPNrP???1:5+1+0:5+0:5+1+1:5+0 ]?10+10 \?10+1 \?7+1 \?7+7 \?I+1+6?J+1+6?]I7qJ\I+J??8+I+*:*???I+1+7?0\7+I>1\I+7?^]I\I+1?8+6pI+*:*???\ \\??P>_POLCLR?I+7+1+1?\I+1X?κX+8j0?X+8X?Xo0?7qI\P+1?X\P+8qI??1+1 \?1+1 \??*PXj*?11C?P>_SPAFP0?_SP1 OPOLDIFOMK>_POLCLR?L+1+\I+1+\J+1p1?\I+Lq\J+L\K+L?ro0?Lq1\K+1? QPOLDSPQO8>_POLCLR?9>_POLCLR?\7+1p1A?\10+1p1B?AkB??8>_POLCLR??Bj1@\10+1o0??8>_POLCLR?1\10+1+\+7+8\?7>_POLCLR?1A??8>_POLCLR?AqB\8+1?Bq1\9+1?AnB?9>_POLCLR?\7+A\10+B?r+\+10+9\?\10+1\9+1?\7+A\10+B\8+AqBp1?K+B+1+1?\7+AqBpKq\9+K\7+AqBpK??Aq1A????7>_POLNOR?8>_POLNOR? 'POLEQU'%A?*EQUATIONS*+*P1j0*+1+*P2j0*+2+*P1jP2*+3+*SIGN)OF)P1*+4+*SIGN)OF)P2*+5+*SIGN)OF)P1qP2*+6+*EXIT*+7?1?1>_POLRAC??2?2>_POLRAC??3??16C?1>_SPAFP0?^+^+*j*?Cp1C?2>_SPAFP0?_SP1?1I>2J>3K?_POLDIF?3>_POLRAC??4?1>_POLSGNSP??5?2>_POLSGNSP??6?1I?2J?3K?_POLDIF?3>_POLSGNSP??7? POLETUDE_POLCHX?Pl2>??u??*P:*?1+2+P?PI?3J?_POLDERSP?3>_POLAFF?3>_POLSGNSP>_POL3?]3A?8B?Pj1?*^*^?Pj2?*^*^??_POLTABV POLFACT1rK??*FACTOR*?*XqbjX*?Ao0??5C>0J>A>_SPAFC??8>_POLCLR?\K+1J?Jq1\8+1?\K+Jp1\8+J?I+Jq1+1+1?\K+Ip1pA\8+Ip1X?βXk1;10??0\8+I??X\8+I???8+K >_POLCOP?A>_POLMF2 POLFACT2rK?1I?\K+Ij0?Ip1I??Iq1I??*FACTOR*?*)))X*?Il1??2+5+**?2+6+I??_SP2?\K+1qI\K+1?J+1+\K+1p1?\K+JpI\K+J??I>_POLMF3 POLFACTOu??*FACTORIZATION?0C?\11+1o0@\11+1+8o1??1F?11>_SPAFP0???I+12+16?\I+1o0??^+^+**?Cp1C>1F?I>_SPAFP0?^+^+**?Cp1C?\I+2j2??^+^+* *?Cp1C??\I+2l2??^+^+**?Cp1C?^+^+\I+2?Cp1C????_SP1 BPOLINILFB@10+7 \?16+7 \?10+1 \?16+2 \?I+1+16?1\I+2? fPOLMEMOfdA?u??*STO)TO*+*P1*+1+*P2*+2+*P3*+3+*EXIT*+4?1>1I>B?2>2I>B?3>3I>B?4>?B?10+I ?_POLCOP POLMENU10+7 \?15+7 \?10+1 \?15+1 \?1P?A?u??*PX*+*DEF)POLY*+1+*EQUATIONS*+2+*DERIVATIVE*+3+*INTEGRAL*+4+*VALUE*+5+*STUDY*+6+*EXIT*+7??1>_POLDEF>A?2>_POLEQU>A?3>_POLDER>A?4>_POLPRI>A?5>_POLVAL>A?6>_POLETUDE>A?7>? +POLMF1+)rI?11J?\J+1j0?1pJJ??I+J >_POLCOP POLMF2~rI?11J?\J+1j0<\J+2j1@\J+1jI@\J+1j1?1pJJ??\J+1j0??1\J+2?I\J+1?1\J+1??\J+2p1\J+2? 4POLMF342rI?11J?\J+1j0?Jp1J??I\J+1?1\J+Ip1? 5POLMF453rI?\11+1j0??I\11+1??\11+1I\11+1? FPOLMF5FDrI?11J?\J+1j0?1pJJ??1\J+3?0\J+2?I\J+1?2\J+1 POLMSG1?*ROOTS)OF)P*?1+13+r zPOLMULzxK>_POLCLR?\I+1X?\J+1Y?Xk0_POLAFF?_POLMEMO TPOLPRISPTRJ>_POLCLR?\I+1k0??L+2+\I+1p2?\I+Lq1Lq1\J+L??\I+1p1\J+1 POLR0C?*?*?4>_SPAFP0?^+^+*j0*?_SP1?\4+1D?Dj1??*SjR*???Dj0??*NO)SOLUTION*?\4+1>_POLMF4?_SP2???Dj1??_POLR1????\4+1j0??_POLR0????Dj2??_POLR2????Dj4@\4+2p\4+4k1;8??_POLR5????_POLCHSEV?Ak3??_POLR4????Dj3??_POLR3?????*FAIL*? UPOLR0US?*OBVIOUS)SOL:?0>_POLAJOUT?4>_POLFACT2??\4+1j0??\4+1>_POLMF4???4>_POLR =POLR1=;4>_POLMF1??*DEGREEj1+)XjBA?\4+1\4+2??_POLAJOUT? :POLR2:8A+1+100>??*DEGREEj2?\4+1C?\4+2B?\4+3A?B q4ACD?*DISCRj?D?Dk0??*NO)SOLUTION?_SP1?4>_POLMF1????Dj0??*XjqB2A*?B2A?_POLAJOUT?X>_POLMF2?X>_POLMF2?A>_POLMF4????*DISCRl0?*1)XjqBqD2A?BqD2A?_POLAJOUT?X>_POLMF2?*2)XjqBpD2A?BpD2A?_POLAJOUT?X>_POLMF2?A>_POLMF4 POLR3_POLCHSOL?_POLR4 3POLR431A>_POLAJOUT?4>_POLFACT1??*ROOTS)OF)QX?_POLR 1POLR51/?*PERFECT)SQUARE*?\4+1C?\4+3B?\4+5A?B q4ACD?*DISCRj*?D?Dk0??*NO)SOLUTION?4>_POLMF1?_SP1????Dj0??*X jqB2A*?B2AZ?Z?2E?_POLR5SP?A>_POLMF4????*DISCRl0?_SP1?*1)X jqBqD2A?BqD2AZ?Z?1E?_POLR5SP?*2)X jqBpD2A?BpD2AZ?Z?1E?_POLR5SP?A>_POLMF4?? POLR5SPZk0??*IMPOSSIBLE?Z>_POLMF5?E\J+2?_SP1???Z>_POLMF2?Ej2??Z>_POLMF2??Z>_POLAJOUT??Z>_POLMF2?Ej2??Z>_POLMF2??Z>_POLAJOUT?? POLRACr+4 ?_POLCOP?1;12+1;12 ]?_POLINILF??*SOLVING*?_POLR??*SOLUTIONS?ε]j2??*NO)SOLUTION*??I+1+]q2?]Ip1?Ip1+1+*X*?Ip1+2+I???_SP1 POLSAIrP?P>_POLCLR?>>~ >t?4+32+*b*?4+60+*2*?10+0+*PXj)Ab)X)p:::pA2)X)pA1)XpA0*?*bj*+D?D\P+1?I+D+0+1??*VALUE)OF)A*?1+11+I?**+C?C\P+Ip1??u??P>_POLAFF POLSGN_POLCHX??P>_POLSGNSP? POLSGNSPr]1?]1>_POLRAC?_POLFACTO?_POLT1??*SIGN):::?\14+1j0@\13+1o0??*FACTOR)1?12>_POLT2?*FACTOR)2?13>_POLT2?*PRODUCT??]1>_POLT2?_POLTABS -POLT1-+1L?4+2]q1 \?I+1+4?0\I+1??] POLT2rI?\?L+r2 \?\I+1n1??*#\I+JXJq1+J+2+\I+1p1+1p\I+1*^??*\I+1*^??K+2+]?]KA?]Kq1B?ApB2C?β^Ak1;10??0\L+2Kq1??2\L+2Kq1??^Cl0<\I+22j0??1\L+2Kq2??1\L+2Kq2???I\L+1?4\L+2]q1?**^?Lp1L IPOLTABSIG_PTINI?0A?\]?Aj]1?Ap1A?8AB?_PTABS???0+0+A+] ]?_PTCOMS vPOLTABVvt\]?]1A?]2B?Al1?\+A+1\?1+B \?0\1+1?_PTINI?1A?8B?_PTABS?16B?_PTABV?0+0+2+] ]?_PTCOMV APOLVALA??*VALUE)OF)P*?1+11+P?X??Pj1?^?Pj2?^?Pj3?^?_SP1 PTABS1I?_PTTV?_PTTH?12I>_PTTV?K+2+J?12pKq1EI?\A+KX?Xj0??B+I+*0*?Ip1+24qB?Ip1+30qB??Xj1?B+I+*p*?Xj1?B+I+*q*?Xj3?_PTDB?Xj2_PTTV?K+2+J?12pEKq1I?\1+KW?Wj1?_PTFH?Wj1?_PTFB?Wj3?_PTDB?Wj2_SPAFP0?^+^+**?Cp2C?^+^+W???16C?\X+1>_SPAFP0? SPTCSQ8]1p3X?13p2E]2q1+6Y??A+2+Xq2+Xp2?A+Y??A+Yq2+Yp2+c ?X+A? WPTCOMSWU1]2?0Z>?1??2+1+*USE)CURSOR)KEYS)FOR)VALUES+)THEN?4+1+*ENTER)TO)GO)ON??]2j0@]1l0?_PTAFF??]1j0@]2l0?_PTVALX??_PTC?0Z>0T>1U?Zl0?Z?1pTT?κT5j0??X+Y?UU???Uj1?X+Y?_PTC??Zj105??Zj24@]2l0?]2q1]2?Zj25@]1l0?]1q1]1?Zj26@]2k]4?]2p1]2?Zj34@]1k]3?]1p1]1??1? PTCOMV2]1?1]2?8+4+*F*?16+4+*F*??0Z>?1???_PTVALXY??_PTC?0Z>0T>1U?Zj105_SPCVFRAC?rX?ε]j2??_SPAFPQ??_SPAFDEC??? ]SPAFDEC][??Xn0:01@Xk100??f?s4?^+^+X?Cp5C?Xn1?Cp1C?Xn10?Cp1C??g?s5?^+^+X?Cp10C??f?i (SPAFINT(&^+^+X?Xj0??Cp2C??CpXp1C? SPAFP0rI?1F?\I+1D?Dj1??^+^+0????J+D+0+1?\I+Jp1X?βXn10[??X>_SPAFC?0F?Jl0??Cp1C?Jj1??^+^+*X*?Cp1C??^+^+*X*?Cp2C?^+^+J?Cp1C???^j8??0C?8+14+*:::*????? hSPAFPQhf]1X?^+^+X?Xj0??Cp2C???CpXp1C?]2X?Xj1??^+^+**?1pCC?^+^+X?CpXp1C? %SPAFRAC%#^+^+**?Cp1C?X2+0X?_SPAFINT CSPCVFRACCA0+1+1+r+r+1+r+r+r ]?β]7q]9m[?1?β]7q]9m[]8?1?Ҳ]8q]5]6m[<]6l500?1]7q]9]7?r]9?]4rp]3]5?]4]3?]5]4?]2]9p]1]6?]2]1?]6]2??1?]8k0?]5]5?]6m500??]5+]6 ]?]1]2??]8 ]?]1? ISPGRADUIG1c?1c?c qc l15?5c?c qc l15?5c?c qc l50?10c?c qc l50?10c