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----MATHEMATICALTERMS(Part1)calculus微积分definition定义theorem定理lemma引理corollary推论prove证明proof证明show证明solution解formula公式ifandonlyif(iff)当且仅当xXforallxXxXthereexistsanxXsuchthat使得given已知set集合finiteset有限集infiniteset无限集interval区间openinterval开区间closedinterval闭区间neighborhood邻域number数naturalnumber自然数integer整数oddnumber奇数evennumber偶数realnumber实数rationalnumber有理数irrationalnumber无理数positivenumber正数negativenumber负数----mapping映射function函数monotonefunction单调函数increasingfunction增函数decreasingfunction减函数boundedfunction有界函数oddfunction奇函数evenfunction偶函数periodicfunction周期函数compositefunction复合函数inversefunction反函数domain定义域range值域variable变量independentvariable自变量dependentvariable因变量sequence数列convergentsequence收敛数列divergentsequence发散数列boundedsequence有界数列decreasingsequence递减数列increasingsequence递增数列limit极限one-sidedlimit单侧极限left-handlimit左极限right-handlimit右极限TheSqueezeTheorem夹挤定理infinity无穷大infinitesimal无穷小equivalentinfinitesimal等价无穷小infinitesimalofhigherorder高阶无穷小orderofinfinitesimal无穷小的阶infinitesimalsofthesameorder同阶无穷小----increment增量continuousfunction连续函数continuity连续性f(x)iscontinuousatx在x连续f(x)isdiscontinuousatx在x间断discontinuity间断点discontinuityofthefirst(second)kind第一（二）类间断点removablediscontinuity可去间断点jumpdiscontinuity跳跃间断点infinitediscontinuity无穷间断点intermediatevalue介值TheIntermediateValueTheorem介值定理zeropoint零点TheZeroPointTheorem零点定理root根equation方程uniformcontinuity一致连续derivative导数rateofchange变化率velocity速度instantaneousvelocity瞬时速度tangent(line)切线normal(line)法线slope斜率left-handderivative左导数right-handderivative右导数f(x)isdifferentiableatxf(x)在x处可导(可微)differentiation求导TheChainRule链式法则differentiationformulas求导公式implicitfunction隐函数explicitfunction显函数----implicitdifferentiation隐函数求导logarithm对数Logarithmicdifferentiation对数求导法parameter参数parametricequation参数方程parametriccurve参数曲线hyperbolicfunction双曲函数hyperbolicsine双曲正弦hyperboliccosine双曲余弦hyperbolictangent双曲正切hyperboliccotangent双曲余切MATHEMATICALTERMS(Part2)differential微分differentialquotient微商approximatevalue近似值error误差relativeerror相对误差absoluteerror绝对误差invarianceofdifferentialform微分形式不变性higherderivative高阶导数firstderivative一阶导数secondderivative二阶导数thirdderivative三阶导数nthderivativen阶导数twicedifferentiable二阶可导acceleration加速度meanvalue中值TheMeanValueTheorem中值定理Rolle’sTheorem罗尔定理Lagrange’sMeanValueTheorem拉格朗日中值定理Cauchy’sMeanValueTheorem柯西中值定理equality等式inequality不等式----indeterminateform不定型(未定式)indeterminateformoftype00()00()型未定式L’Hospital’sRule洛必达法则Taylor’sformula泰勒公式polynomial多项式nth-degreepolynomialn次多项式remaind余项Lagrange’sformofremainder拉格朗日型余项Peano’sformofremainder皮亚诺型余项Maclaurinformula麦克劳林公式Taylorpolynomial泰勒多项式Mauclaurinpolynomial麦克劳林多项式polynomialapproximation多项式逼近accuracy精确度margin边际marginalcost边际成本marginalrevenue边际收益elasticity弹性density密度mass质量extremevalue极值localmaximumvalue极大值localminimumvalue极小值(absolute)maximum最大值(absolute)minimum最小值stationarypoint驻点（稳定点）criticalpoint...