极限的保号性

*121．3410002．3424001、、．．O171A1004－8332201103－0007－03．、、．111．11ⅰlimn→∞an=aa＞0N＞0n＞Nan＞0．ⅱlimn→∞an=aa＜0N＞0n＞Nan＜0．1．22Ⅰlimn→∞an=a＞a'＞0N＞0n＞Nan＞a'．Ⅱlimn→∞an=a＜a'＜0N＞0n＞Nan＜a'．ⅠⅰⅠ．limn→∞an=a＞0limn→∞an=a＞a2＞0ⅠN＞0n＞Nan＞a2＞0ⅰ．ⅰⅠⅰ．limn→∞an=a＞a'＞0bn=an－a'limn→∞bn=limn→∞an－a'=a－a'＞0．ⅰN＞0n＞Nbn＞0an＞a'Ⅰ．Ⅱⅱ．．222．11ⅰN＞0n＞Nan0limn→∞an=alimn→∞an=a0．ⅱN＞0n＞Nan0limn→∞an=alimn→∞an=a0．2011№．3JournalofGannanNormalUniversityJune．2011*2011－02－22GJJ083881964－、．2．22anbnN0n＞N0anbnlimn→∞anlimn→∞bn．2．12．2anbnN0n＞N0anbn．cn=bn－ann＞N0cn02．1limn→∞cn＞0limn→∞anlimn→∞bn．2．2．2．22．12．2bn=02．1．．331．11ⅰlimn→∞an=aa＞0N＞0n＞Nan＞0．ⅱlimn→∞an=aa＜0N＞0n＞Nan＜0．2．12ⅠN＞0n＞Nan0limn→∞an=alimn→∞an=a0．ⅡN＞0n＞Nan0limn→∞an=alimn→∞an=a0．1．12．11．2．11．1limn→∞an=aa＞0．．k＞0nk＞kank02．1limk→∞ank=a0．1．1．1．12．1．4．44．11limx→x0fx=A．limx→x0fx=A＞0A＜0δ＞00＜|x－x0|＜δfx＞0fx＜0．4．21limx→x0fx．δ=1n＞0nxn0＜|xn－x0|＜1nfxn0fxn0limx→x0fx=A0A0．4．24．1．5．55．11limx→x0fx．δ＞00＜|x－x0|＜δfx0fx0limx→x0fx=A0A0．5．22limx→x0fxlimx→x0gxδ＞00＜|x－x0|＜δfxgxlimx→x0fxlimx→x0gx．5．15．22．12．2．611．111．22．．22．22．3．35．24．1820115．4．15．14．1．limx→x0fx=A．δ＞00＜|x－x0|＜δfx0．5．1．limx→x0fx=A＜04．1δ1＞00＜|x－x0|＜δ1fx＜0．δ=minδδ10＜|x－x0|＜δfx＜05．1．4．25．1．．44．12．1．2．14．12．1．limx→x0fx=AA＞0．4．1．δ=1n＞0nxn0＜|xn－x0|＜1nfxn0xnlimn→∞xn=x0fxn0．limx→x0fx=A1limn→∞fxn=A．2．1A04．1．54．113．32．2．14．14．15．22．11．11．2．1．M．200123－30．2．M．200128－33．SomeNotesonthePropertiesofGuaranteeingSignandGuaranteeingInequalityXUShao-yuan1ZHONGZheng-yan21．SchoolofMathematicsandComputerScienceGannanNormalUniversityGanzhou341000China2．TheThirdMiddleSchoolinXingguoGanzhou3424001ChinaAbstractInthispaperweshowtheequivalenceofthepropertiesofguaranteeingsignandguaranteeinginequalityforlimitationofthesequenceofnumber．Furthermorewediscusstherelationshipsbetweenthepropertiesofguaranteeingsignandguaranteeingine-qualityforthelimitofthesequenceofnumberandthelimitoffunction．Theseresultsaretheusefulandindispensablesupplementstotherelatingcurrenttextbooksforthecollegestudentsoncampus．Keywordslimitfunctionpropertyofguaranteeingsignpropertyofguaranteeinginequality93