高等数学英文板总结（精选合集）.docx

高等数学英文板总结（精选合集）

第一篇：高等数学英文板总结函数Inmathematics,afunctionisarelationbetweenasetofinputsandasetofpermissibleoutputswiththepropertythateachinputisrelatedtoexactlyoneoutput.极限Inmathematics,alimitisthevaluethatafunctionorsequence“approaches”astheinputorindexapproachessomevalue.Theconceptofalimitofasequenceisfurthergeneralizedtotheconceptofalimitofatopologicalnet,andiscloselyrelatedtolimitanddirectlimitincategorytheory.Informulas,alimitisusuallydenoted“lim”asinlimn→c(an)=L,andthefactofapproachingalimitisrepresentedbytherightarrow(→)asinan→L.Supposefisareal-valuedfunctionandcisarealnumber.Theexpressionlimf(x)Lxcmeansthatf(x)canbemadetobeasclosetoLasdesiredbymakingxsufficientlyclosetoc.无穷小InfinitesimalIncommonspeech,aninfinitesimalobjectisanobjectwhichissmallerthananyfeasiblemeasurement,butnotzeroinsize;or,sosmallthatitcannotbedistinguishedfromzerobyanyavailablemeans.无穷大连续函数Inmathematics,acontinuousfunctionis,roughlyspeaking,afunctionforwhichsmallchangesintheinputresultinsmallchangesintheoutput.介值定理Inmathematicalanalysis,theintermediatevaluetheoremstatesthatifacontinuousfunctionfwithaninterval[a,b]asitsdomaintakesvaluesf(a)andf(b)ateachendoftheinterval,thenitalsotakesanyvaluebetweenf(a)andf(b)atsomepointwithintheinterval.Thishastwoimportantspecializations:Ifacontinuousfunctionhasvaluesofoppositesigninsideaninterval,thenithasarootinthatinterval(Bolzano'stheorem).[1]And,theimageofacontinuousfunctionoveranintervalisitselfaninterval.导数Thederivativeofafunctionofarealvariablemeasuresthesensitivitytochangeofaquantity(afunctionordependentvariable)whichisdeterminedbyanotherquantity(theindependentvariable).Supposethatxandyarerealnumbersandthatyisafunctionofx,thatis,foreveryvalueofx,thereisacorrespondingvalueofy.Thisrelationshipcanbewrittenasy=f(x).Iff(x)istheequationforastraightline,thentherearetworealnumbersmandbsuchthaty=mx+b.miscalledtheslopeandcanbedeterminedfromtheformula:mchanginyy，wherechanginxxthesymbolΔ(theuppercaseformoftheGreekletterDelta)isanabbreviationfor“changein”