Algebra and Trigonometry Review Material

Algebra and Trigonometry Review Material

Algebra and Trigonometry Review Material Department of Mathematics Vanderbilt University June 2, 2004 http://atlas.math.vanderbilt.edu/~pscrooke/calculus/calculus.html ¡ ¢ £ ¤ ¢ £ ¥ ¦ § ¨ © ¨ ¨ ¦ © ! 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B » · = Ä @ Å ¶ · = @ B Q G L HGLK QDEFGH e I L JO QP OQ PRG HGLK K QGT g G LQ OQI VGH PI V IPLQ G WHOE 1 S 1 1 1 S S 1 1 1 S PRG OH U Q T g R R g G LKK PRG OW e LQV VGQOPG FM fe f Y 1 1 1 S S ¨ ¨ |y| |x| Æ Æ È Ç Ç É Æ Æ È Ç Ç É y x -4 -3-2 -10 1 2 3 4 UDHG h Y « k j R G LFIOKDPG NLKDG I PRG V IPLQ G WHOE PRG OH U Q 1 1 1 S 1 1 W PRG QDEFGH e I JOI P NGT PRGQ fe f I G t D L K PO PRG QDEFGH PIGKW f_ f ] _ Y W PRG QDE¡ 1 1 1 1 1 FGH I QGULP NGT ILM e ] q _ T PI V IPLQ G fe f WHOE PRG OH U Q I _Y COPG PRLP Q PR I LIG PRG 1 1 1 1 S 1 1 1 1 1 S LFIOKDPG NLKDG fe f ] _ I PRG QGULP NG OW e ] q _ T QLEGKM fe f ] f q _ f ] _ ] q q _ ] q e Á 1 1 IO W e I QGULP NGT fe f ] q e Y j R G KLIP G t D L K PM I L F P L g g L H V I Q G fe f I QGNGH QGU¡ 1 1 1 1 1 1 | 1 S 1 © LP NGT FDP g G QGGV PRG E QDI I UQ Q WHOQP OW e T I Q G e RLI LQOPRGH QGULP NG I UQ ¨ Q 1 1 1 1 1 S 1 1 1 a PÁ PR I g L M PRG P g O QGULP NG I UQI LQ GK ODP LQV g G UGP L JOI P NG ODP OE GY O g G LQ 1 1 1 1 S S 1 1 S S V G Q G PRG LFIOKDPG NLKDG OW L QDEFGH e L I k e W e Ê r 1 fe f ] u q e W e r 1 ËGHG LHG IOE G JHOJGHP GI OW PRG LFIOKDPG NLKDG PRLP ROKV WOH LKK HGLK Q D E F G H I k 1 ZDKG L E JKG f q f ] f f f q _ f ] f_ f T FG LDIG PRGM FOPR G t D L K _Y S f f ] f f À f f f q _ m f ] f q _ f À fm fT FG LDIG FOPR G t D L K b Y S f f _ f_ f _ ] ] T I Q G PRGM FOPR G t D L K Y 1 S f f q m f q m f m x x x x x x x x x x x x x x f ¤ f f f ¤ f f fa ¤ q m f fa f ¤ f q m fT I Q G h Y 1 S © # ª L fh q } _ f ] q h q } _ T I Q G h q } _ I QGULP NGY 1 S 1 1 } } } } _ q f_ q f_ q f_ q _ _ f _ f _ f F ] ] ] ] h Y x x } } } } _ q _ f _ q _ f f q _ q _ f f_ q _ f x x x x x x x x W Ê _T Q V f q h f Y © ( ª Q G Ê _T g G UGP Ê h Y O q h Ê r T QLEGKM q h I QOQ¡QGULP NGY j R D I T 1 S 1 1 f q h f ] q h Y fe Ì ¤ h f ] e Ì ¤ h T I Q G e Ì ¤ h I JOI P NG WOH LKK NLKDGI OW e Y 1 S 1 1 1 © % ª Y « fe f ¤ _ W e q m T LK DKLPG S S © ª x x x x ] « fe f ¤ _Y C O g T I Q G e I QGULP NGT fe f ] q e Á « fe f ¤ _ Q G « fe f ¤ _ I JOI P NGT 1 S 1 1 1 S 1 1 1 x x x x IOT « fe f ¤ _ ] « q e ¤ _ ] q « e ¤ _Y x x x x « QV LKK NLKDGI OW e ID R PRLP fe f ] m Y 1 S © Í ª ZG LKK PRLP fe f ] m I PRG V IPLQ G WHOE e PO PRG OH U Q T IO e LQ FG OQKM q m OH m T S 1 1 S 1 1 S QLEGKM e ] Î m Y QV LKK NLKDGI OW e ID R PRLP f_ e q « f ] Y 1 S © ¦ Ï ª ZG LKK PRLP f_ e q « f ] I PRG V IPLQ G WHOE _ e q « PO PRG OH U Q Á IO _ e q « LQ FG S 1 1 S 1 1 S OQKM q OH T QLEGKM _ e q « ] Î Y O T _ e q « ] q OH _ e q « ] T QLE GKM _ e ] q _ OH _ e ] h _ Y O e ] q h OH e ] b Y j R G IGP Ð e fe f _ Ñ OQPL QI LKK QDEFGHI OQ PRG HGLK K QG PRLP LHG KGII S 1 1 © ¦ ¦ ª x PRLQ _ DQ PI L g L M WHOE PRG OH U QY 1 1 1 x x Ò Ò Ô Ó Ó Õ Ò Ò Ô Ó Ó Õ -4-3 -2 -1 0 1 2 3 4 UDHG h Y b k j R G IGP e fe f _ Y 1 Ð Ñ x x x fe f Ö _ Ñ OQPL QI LKK QDEFGHI OQ PRG HGLK K QG PRLP LHG EOHG j R G IGP.

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