函數(shù)ppt-advancedmathematicsd-資料下載頁
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【導讀】Introduction. LearnEnglish. CalculateAnalysis. StaticDynamic. PhilosophyArts. LogicalImage. Deducestepbystep. Exercise. Functions. Limites. Derivatives. Integration. Whatisafunction?intheMiddleSchool?Variables:x,y. Valueorimage. Relation. Determination. Region. Verbally. (0)3,(1)4,West(1)=30,West(2)=38,West(3)=32,West(4)=31,x. Age(Name):. Age(John)=18,Age(Linda)=17…BirthDay(Name):. BirthDay(John)=02/04/1995,BirthDay(Linda)=16/07/1996,…Sex(Name):. Sex(John)=M,Sex(Linda)=F…{John,Linda,……}
【正文】 Relations of Trigonometric Functions ? 1111121212si n c os / 2si n( si n ) , c os( c os )c os( si n ) 1si n( c os ) 1t a n( si n )1xxx x x xxxxxxxx??????????????????Exponential amp。 Logarithmic Functions ?We know ?Question: what is And ?We can use a sequence to define it: ?A function of the form , is called an exponential function with base b. 2 3 1 / 2 0. 01 3. 272 , 2 , 2 , 2 , 2 .. .. .. .. .. .. .?2?? 2 , ( , ) ?x x ? ?? ?3. 1 3. 14 3. 141 3. 1415 3. 141592 , 2 , 2 , 2 , 2 , ...... .. 0?, ( 0 )xy b b??Properties of Exponential Function ?The graphs are all pass (0,1) 1 1 ,1 i nc r e a si ng ,1 de c r e a si ng .bybyby? ? ?????Natural exponential function ? ?The number of e es from the limitation of , 2 , 7 1 8 2 8 1 8 2 8 .. .. .. .. .. , e x p ( )xe e x?( 1 1 / ) ,xy x w he n x? ? ? ?Logarithmic Function ?A logarithmic function with base b (b0,b≠1) is an inverse of a exponential function: ?Logarithmic function with e is called natural logarithmic function, noted as ln(x) l ogy bx b y x? ? ?Algebraic Properties of Logarithms ? l og ( ) l og ( ) l og ( )l og ( / ) l og ( ) l og ( )l og ( ) l og ( )l og ( 1 / ) l og ( )b b bb b brbbbbac a c pr od ucta c a c qu ot i e nta r a po w e rc c rec i pr ocal???????Change Base Formula ? lnl o glnbxxb?Parametric Equation ?Graph can be explained also by parametric equation, ?ex: a circle in Cartesian Coordinates is not a function ?However, the circle in Polar Coordinates system : is a function ?The circle can also expressed by parametric equation: 21yx? ? ?1r ?( , )r ?( , )xys in( 0 , 2 )c o sxttyt???????Parametric Equation ?Roserhodoneacurve s i n ( / )r n d ??Parametric Equation ?Escher’s famous art work “Path of Life” Reference ?James Strewart, Calculus, Thomson Leaning
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