**TI86** Program file dated 06/23/04, 19:56 ¶ ¦THEOREMS¦¤Ç4SZ 3ioØ3iQD370o9ZDEFINEoàToD0 3Koìoé-MATH TUTOR skramstadoëD2/D4/-Ver. 1,(c)1999oëD4/D4/-F1 ALGEBRAoëD5/D4/-F2 TRIGONOMETRY F3 CALCULUSoëD7/D4/-F4 PHYSICSoLD1/-F1/4T1/D2/-F2/4T2/D3/-F3/4T5/D4/-F4/4T6/D5/4QU/3QoàQo6ZMAKoãoàT6o9ZTHEOR6oØ3KPD1náùQoáToàT5oD0 3KoìoëD1/D7/-CALCULUSoëD3/D1/-F1 GENERALLY F2 GROWTH & DECAYoëD5/D1/-F3 DERIVITIVES F4 ANTIDERIVITIVESoLD1/-F1/5T10/D2/-F2/4T7/D3/-F3/4T3/D4/-F4/4T4/D5/4EX/3ToàT10oìoëD1/D7/-CALCULUSoëD3/D1/-F1 APPLICATIONS F2 TAYLOR SERIESoëD5/D1/-F3 FOURIERoëD6/D1/-F4 DIFFERENTIAL EQS.oëD7/D1/-F5 `6EXIToLD1/-F1/4T8/D2/-F2/4TT/D3/-F3/4TF/D4/-F4/4TD/D5/4EX/4T5oàTDo:ZTHEORTDnØ3KPD1náùQoáõT10oàTTo:ZTHEORTTnØ3KPD1náùQoáõT10oàTFo:ZTHEORTFnØ3KPD1náùQoáõT10oàT7o9ZTHEOR7nØ3KPD1náQoá(T5oàT8o9ZTHEOR8nØ3KPD1náùQoáõT10oàT1oD0 3KoìoëD1/D7/-ALGEBRAoëD3/D1/-F1 FACTORING F2 EXPONENTS & LOGSoëD5/D1/-F3 SERIESoëD6/D1/-F4 COMPLEX NUMBERS F5 `6EXIToLD1/-F1/4A1/D2/-F2/4A2/D3/-F3/4A3/D4/-F4/4A4/D5/4EX/3ToàA4o:ZTHEOR1CoØ3KPD1náùQoá‰T1oàA3o:ZTHEOR1AoØ3KPD1náùQoá‰T1oàA1o9ZTHEOR1oØ3KPD1náùQoá‰T1oàA2o7ZINITo4ZLoŽD0/D25/-EXPONENTS AND RADICALSoŽ+D51/D124 2xnŽ+D2/D6 2yo6ZLINoŽD10/D0/-A^0=1, A0: A^x/A^y=A^(x-y)oŽD16/D0/-(A/b)^x=A^x/b^x: A^x=1/A^xoŽD22/D0/-(A^x)^y=A^(xy): A^(x)*A^y=A^(x+y)oŽD28/D0/-(Ab)^x=A^(x)*b^x: A=A^(1/2)oŽD34/D0/-Í(A^y)=A^(y/x)=(ÍA)^yoŽD40/D0/-Í(Ab)=ÍA*Íb: ÍA=A^(1/x)oØÇ4SZQD370oãoŽ*D56a2y/2x 3ioØ3iPD1o-1 3soØ3iUD1o-0 3soØ4SZ/2xaD49`D74D6a2y/D1U3snãoLD1/4MO/5A2A/D2/4PR/4T1/D4/4EX/4T1/D5/4QU/3QoàA2Aoƒo4ZLoŽD0/D0/-Í(A/b)=ÍA/ÍboŽD6/D0/-log 10=1oŽD12/D0/-log Ab=log A+log boŽD18/D0/-log A^x=x*log AoŽD24/D0/-log (A/b)=log A-log b, THESE logoŽD30/D0/-RULES APPLY TO LOGARITHMS OF ANYoŽD36/D0/-BASE. THE LOG n OF BASE n=1.oŽD42/D0/-LOGS OF BASE e ARE CALLEDo4ZKoLD1/4MO/5A2B/D2/4PR/4A2/D4/4EX/4T1/D5/4QU/3QoàA2Boƒo4ZLoŽD0/D0/-natural logarithmns, REPRESENTEDoŽD6/D0/-BY KEY [LN] ON THIS MACHINE.oŽD14/D0/-logoŽD14/D20/-x=c THEN 10^c=xoŽD17/D11/-10oŽD25/D0/-ln x=c, THUS e^c=x. e^x=(e^x)^xoŽD34/D0/-TO FIND x IN A^x=b, TAKE THEoŽD40/D0/-(log b)/(log A)=x. HANDY FOR FINDINGo4ZKoLD1/4MO/5A2C/D2/4PR/5A2A/D4/4EX/4T1/D5/4QU/3QoàA2Coƒo4ZLoŽD0/D0/-THE LENGTH OF TIME REQUIRED BYoŽD6/D0/-BY EXPONENTIAL GROWTH/DECAYoŽD12/D0/-FUNCTIONS TO REACH A KNOWNoŽD18/D0/-QUANTITY.o4ZKoLD2/4PR/5A2B/D4/4EX/4T1/D5/4QU/3QoàA3oáT1oàT2oD0 3KoìoëD1/D5/-TRIGONOMETRYoëD3/D1/-F1 SINE LAW-TRIANGLE F2 2D SHAPES & SOLIDSoëD5/D1/-F3 IDENTITIES F4 HYPERBOLIC SINE F5 `6EXIToLD1/-F1/4B1/D2/-F2/4B2/D3/-F3/4B3/D4/-F4/4B4/D5/4EX/3ToàB1o6ZTRIoØ3KPD1náùQoá ¥T2oàB2o9ZTHEOR2oØ3KPD1náùQoá ¥T2oàB3o7ZINITo4ZLoŽD0/D0/-TRIG IDENTITIESo6ZLINoŽD9/D0/-sin(x+y)=sin x*cos y+sin y*cos xoŽD15/D0/-cos(x+y)=cos x*cos y-sin x*sin yoŽD21/D0/-(tanÁ)+1=(1/cosÁ)=secxoŽD27/D0/-(sinÁ)+(cosÁ)=1oŽD33/D1/-tanÁ=sinÁ/cosÁoŽD33/D65/-360=2Ä RADIANSoŽD39/D0/-Ä/2 RADIANS=90o4ZKoLD1/4MO/5B3A/D2/4PR/4T2/D4/4EX/4T2/D5/4QU/3QoàB3Aoƒo4ZLoŽ+D51/D124 2xnŽ+D2/D6 2yoŽD0/D0/-sin (2Á)=2sinÁ*cosÁoŽD7/D0/-cos(2Á)=cosÁ-sinÁoŽD14/D0/-sinÁ=.5(1-cos(2Á))oŽD21/D0/-cosÁ=.5(1+cos(2Á))oŽD28/D0/-cos(x+y)=sin x*sin y-cos x*cos yoŽD35/D0/-1/sin x=1/(tan x*cos x)=CoSeCant xoØÇ4SZQD370oãoŽ*D56a2y/2x 3ioØ3iPD1o-1 3soØ3iUD1o-0 3soØ4SZ/2xaD49`D74D6a2y/D1U3snãoLD1/4MO/5B3B/D2/4PR/4B3/D4/4EX/4T2/D5/4QU/3QoàB3Boƒo4ZLoŽD0/D0/-1/cosÁ=SECantÁoŽD7/D0/-1/tanÁ=cosÁ/sinÁ=COTangentÁoŽD14/D0/-1+cotx=cscxoŽD21/D30/-HYPERBOLICS:oŽD28/D0/-coshÁ-sinhÁ=1, sinh 0=0,cosh 0=1oŽD35/D0/-sinhÁ=sinhÁ, coshÁ=coshÁoŽD41/D0/-tanhÁ=sinhÁ/coshÁo4ZKoLD2/4PR/5B3A/D4/4EX/4T2/D5/4QU/3QoàB4o7ZINITo4ZLoŽD0/D0/-sinhÁ=(e^Á-e^Á)/2oŽD6/D0/-cosh x=(e^x+e^x)/2oŽD12/D0/-tanh Á=sinhÁ/coshÁoŽD18/D0/-cosh x IS THE catenary, SHAPEDoŽD24/D0/-LIKE THE CABLES STRUNG BETWEENoŽD30/D0/-TELEPHONE POLES.oØÇ4SZQD370oãoŽ+D51/D124 2xoŽ+D2/D6 2yoŽ*D56a2y/2x 3ioØ3iPD1o-1 3soØ3iUD1o-0 3soØ4SZ/2xaD49`D74D6a2y/D1U3snãoLD2/4PR/4T2/D4/4EX/4T2/D5/4QU/3QoàT3o9ZTHEOR3oØ3KPD1náùQoá(T5oàT4oD0 3KoìoëD1/D4/-ANTIDERIVITIVESoëD3/D1/-F1 GENERALLY F2 ELEMENTARYoëD5/D1/-F3 NON-ELEMENTARYoëD6/D1/-F4 IMPROPER INTEGRALSF5 `6EXIToLD1/-F1/4D1/D2/-F2/4D2/D3/-F3/4D3/D4/-F4/4D5/D5/4EX/4T5oàD5o:ZTHEOR4IoØ3KPD1náùQoáØT4oàD1o:ZTHEOR4AoØ3KPD1náùQoáØT4oàD2o:ZTHEOR4BoØ3KPD1náùQoáØT4oàD3oD0 3KoìoëD1/D1/-NON-ELEMENTARY A.D.soëD3/D1/-F1 INTEGRAL NOTATION F2 TABLE-INDEFINITE INTEGRALSoëD6/D1/-F3 EXAMPLESoLD1/-F1/4D4/D2/-F2/4D9/D3/-F3/5D3X/D4/4EX/4T4/D5/4QU/3QoàD9oD0 3KoìoëD1/D1/-INDEFINITE INTEGRALS F1 e,cos x,sin x,ln xF2 POLYNOMIAL p(x) &oëD4/D4/-ln x,e^x,cos&sinoëD5/D1/-F3 POWERS:sin,cos,tanF4 QUADRATICS IN ()& DENOMINATORoLD1/-F1/4C1/D2/-F2/4C2/D3/-F3/4C3/D4/-F4/4C4/D5/4EX/4D3oàC1o:ZTHEOR4CoáED9XoàC2o:ZTHEOR4DoáED9XoàC3o:ZTHEOR4EoáED9XoàC4o:ZTHEOR4FoàD9XoØ3KPD1náùQoáóD9oàD3Xo:ZTHEOR4GoØ3KPD1náùQoá(D3oàD4o:ZTHEOR4HoØ3KPD1náùQoáD3À®