數(shù)學(xué)專業(yè)英語PPT課件

NewWordsitsaltitude,f(x+h)-f(x),representsthedifferenceoftheordinatesofthetwopointsQandP.,考慮斜邊為PQ的直角三角形，它的高度f(x+h)-f(x)表示P、Q兩點(diǎn)縱坐標(biāo)的差。,Therefore,thedifferencequotientrepresentsthetrigonometrictangentoftheangleathatPQmakeswiththehorizontal.,因此，差商表示PQ與水平線的夾角a的正切。,TherealnumbertanaiscalledtheslopeofthelinethroughPandQanditprovidesawayofmeasuringthe“steepness”oftheline.,實(shí)數(shù)tana叫做直線PQ的斜率，它提供了一種度量直線陡峭程度的方法。,Forexample,iffisalinearfunction,sayf(x)=mx+b,thedifferencequotienthasthevaluem,somistheslopeoftheline.,例如，如果f是一個(gè)線性函數(shù)，那么差商的值為m,那么m就是直線的斜率。,Supposenowthatfhasaderivativeatx.Thismeansthatthedifferencequotientapproachesacertainlimitf(x)ashapproaches0.現(xiàn)在假設(shè)f在x有導(dǎo)數(shù)。這意味著當(dāng)h趨于0時(shí)，差商趨于某一個(gè)極限f(x)。,Whenthisisinterpretedgeometricallyittellsusthat,ashgetsnearerto0,thepointPremainsfixed,QmovesalongthecurvetowardP,andthelinethroughPQchangesitsdirectioninsuchawaythatitsslopeapproachesthenumberf(x)asalimit.,其幾何意義為,當(dāng)h趨于0時(shí),點(diǎn)P保持不動(dòng),而點(diǎn)Q沿曲線趨近P,同時(shí),經(jīng)過PQ的直線以這樣的方式改變方向,即其斜率趨于數(shù)值f(x),并以它為極限.,ForthisreasonitseemsthatnaturaltodefinetheslopeofthecurveatPtobethenumberf(x).ThelinethroughPhavingthisslopeiscalledthetangentlineatP.正因如此，把曲線在P點(diǎn)的斜率定義成數(shù)f(x)看起來是自然的。通過P且具有這個(gè)斜率的直線叫做在P點(diǎn)的切線。,本小節(jié)重點(diǎn)掌握,1.如果差商以某一個(gè)確定的值為極限，則該極限叫做f在x點(diǎn)的導(dǎo)數(shù)。2.通過P且具有斜率f(x)的直線叫做在P點(diǎn)的切線。,Ifthedifferencequotientapproachessomedefinitevalueasalimit，thenthislimitiscalledthederivativeoffatx.,Thelinethro