极限的一些直观介绍 毕业论文外文翻译

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1、英文原文AnIntuitiveIntroductiontoLimitsLimitsisoneofthemostfundamentalconceptsofcalculus.TheconceptofcalculuswasnotthatclearduringthetimeofLeibnizandNewton,butlaterdevelopmentsontheconcept,particularlythedefinitionbyCauchy,Weierstrassandothermathematiciansest

2、ablishedthefirmfoundationofcalculus.Inthediscussionbelow,Iwilltrytointroducetheconceptoflimitsintuitivelyasitappearsincommonproblems.CircumferenceandLimitsIfwearegoingtoapproximatethecircumferenceofacircleusingtheperimeterofaninscribedpolygon,evenwithoutc

3、omputation,wecanobservethatasthenumberofsidesofthepolygonincreases,thebetterourapproximation.Infact,wecanmaketheperimeterofthepolygonascloseaswepleasetothecircumferenceofthecirclebychoosingasufficientlylargenumberofsides.Moreover,nomatterhowlargethenumber

4、ofsidesourpolygonhas,itsperimeterwillneverexceedthecircumferenceofthecircle.Asthenumberofsideofthepolygonsincreases,itsperimetergetsclosertothecircumferenceofthecircle.Inamoretechnicalterm,wesaythatthelimitoftheperimeterofthepolygonasthenumberofitssidesin

5、creaseswithoutboundisequaltothecircumferenceofthecircle.Symbolically,ifweletbethenumberofsidesoftheinscribedpolygon,betheperimeterofapolygonwithsides,andbethecircumferenceofthecircle,wecansaythatthelimitofasisequalto.Compactly,wecanwrite.NumbersandLimitsW

6、eendwithamorefamiliarexampleusuallyfoundinbooks.Whatifwewanttofindthelimitofasapproaches3?Toanswerthequestion,wemustfindthevaluewhereisverycloseto3.Thosevalueswouldbenumbersthatareverycloseto3–someslightlygreaterthan3andsomeslightlylessthan3.Placethevalue

7、sinatablewehaveFromthetable,wecanclearlyseethatasthevalueofapproaches3,thevalueofapproaches7.Concisely,wecanwritethe.英文翻译极限的一些直观介绍极限是一个最基本的概念的演算。微积分的概念在牛顿莱布尼兹时代并不明确，直到后面柯西、魏尔斯特拉斯和其他数学家的定义才奠定了牢固的基础微积分。在下面的讨论中，我将试图引入概念出现在普通问题中的直观极限。圆和极限如果我们要使用多边形近似的计算圆的周长，即

8、使没有计算时，我们能观察到，随着多边形边长数量的增加，它越来越接近圆。事实上，我们能使多边形尽量接近圆的圆周来计算圆的周长。此外，无论有多大的多边形数量，它们永远不会超过周长。作为多边形数量方面的增加,它的周长愈接近的圆周圆更技术性的术语，我们说的多边形边的数量无限接近圆周时，多边形和圆的面积是几乎相等的。一般的，我们设多边形的边数为，为多边形的周长，为圆的周长，我们可以说，当时的极限是.简洁地,我们能写成.值和极限我们通常可