数学专业英语翻译谢谢了摘要泰勒公式是数学分析中非常重要的基本内容,它在函数估计和近似计算方面等广为应用．也是函数的极值、幂级数理论等众多数学理论的基础.泰勒公式的基本
数学专业英语翻译谢谢了
摘要泰勒公式是数学分析中非常重要的基本内容,它在函数估计和近似计算方面等广为应用．也是函数的极值、幂级数理论等众多数学理论的基础.泰勒公式的基本思想是用多项式来逼近一个已知函数，而这个多项式的系数由给定函数的各阶导数确定，并对这种逼近给出有效地估计.因此全面认识泰勒公式尤为重要.本文首先介绍了一元和多元泰勒公式的定义,然后分别从证明中值公式，证明不等式，导数的中值估计,关于界的估计,求无穷远处的极限，中值点的极限，函数的极限，近似计算,函数方程中的应用等方面对泰勒公式的应用做了归纳.关键词：泰勒公式；皮亚诺型余项；拉格朗日余项；麦克劳林公式
Abstract
Taylor'sformulaisthemathematicalanalysisofthebasiccontentisveryimportant,itissimilarinfunctionestimationandcalculationofsuchwidelyused.Isalsoafunctionofextremevaluetheory,andmanyothermathematicaltheoryofpowerseriesbasis.Taylorformulaforthebasicideaistousepolynomialstoapproximateaknownfunction,andthecoefficientsofthepolynomialbythegivenfunctiontodeterminethederivative,andthisapproachgivesaneffectiveestimate.Therefore,comprehensiveunderstandingofTaylor'sformulaisparticularlyimportant.ThispaperintroducestheTaylorformulaofonedollarandmulti-definition,thentheproofofthevaluefromtheformula,respectively,thatinequality,themedianestimatederivatives,onindustryestimates,demandinfinitylimit,themedianpointofthelimitfunctionlimits,approximation,functionequationsandsoonTaylorformulatodotheinduction.
【Keywords】:Taylor'sformula;Peano-typeremainder;Lagrangeremainder;Maclaurinformula
（PS：以上由综合外语团倾情奉献，望楼主满意，O(∩_∩)O~！！）
Taylorformulaisveryimportantinthemathematicalanalysis,itisthebasiccontentinfunctionandwidelyappliedinapproximatecalculation.Also,thefunctionextremevaluetheoryofpowerseries,etc.OfthebasictheoryofmathematicsisthebasicthoughtofTaylorformulawithpolynomialfunctionapproximationtoaknown,butthecoefficientsofpolynomialfunctionbyaderivativeofthisapproach,andareeffectively.ThereforeacomprehensiveunderstandingofTaylorformulaisparticularlyimportant.ThispaperintroducesapluralisticTaylorformulaandthedefinition,thenrespectivelyfromtheproofofformula,totestifyinequality,themedianestimate,derivativeboundaryestimateaboutthelimitsofinfinity,andthelimitvaluepointlimitfunction,approximatecalculation,thefunctionequation,theapplicationofTaylorformulaaspectsofapplication.Keywords:Taylorformula,Morethanskinjarnotype,Lagrangemore,MsMcLaughlinformula