高等數(shù)學(xué)極限習(xí)題100道

1、求極限limsinsinxxxx?021設(shè)，求證：lim()lim()xxxxfxAfxA????00??求極限limcosln()coslnxxx?????1求極限limsinxxx??011求極限limarctanxxxx???2112求極限lim()xxxe???11求極限limarctanarcsinxxx???1求極限limxxx???012122)sin1(sinlimnnn????求數(shù)列的極限??AxfAufuxuxxxu

2、uxx??????????)(lim)(lim)()(lim00000試證：，又，且設(shè)設(shè)試確定實(shí)數(shù)，之值，使得：當(dāng)時(shí)，為無窮??；當(dāng)時(shí)，為無窮大。fxxxabxafxxbfx()ln()()????1設(shè)，問：當(dāng)趨于何值時(shí)，為無窮小。fxxxxfx()tan()?2該鄰域內(nèi)的某去心鄰域，使得在證明：存在點(diǎn)，且，若)()()(lim)(lim000xfxgxABBxgAxfxxxx??????設(shè)，試證明：對任意給定的，必存在正數(shù)，使得對適含不

3、等式；的一切、，都有成立。lim()()()xxfxAxxxxxxfxfx???????????000010201221?????，試用極限定義證明：已知：AxfAxfxxxx?????)(lim0)(lim00??????是否也必發(fā)散？同發(fā)散，試問數(shù)列與若數(shù)列nnnnyxyx?求的表達(dá)式fxxxxnnn()lim??????2121求數(shù)列的極限nnnnnn)1)(1(63lim34???????其中求數(shù)列的極限)1(2lim????a

4、aannn求數(shù)列的極限)11()311)(211(lim222nn??????求數(shù)列的極限limnnn???1000012求數(shù)列的極限limnnnnn??????2243351求數(shù)列的極限lim()nnn????1求數(shù)列的極限limnnnn????123)200(2122lim???????????bbanbnnann且，求數(shù)列的極限求數(shù)列的極限lim()nnnn????1212求數(shù)列的極限lim()nnnn?????1213求極限li

5、mnnnnn??????????2103103102102121，，且的某鄰域內(nèi)若在BxgAxfxgxfxxxxx?????)(lim)(lim)()(000試判定是否可得：BA?是否成立？為什么？，則，若0)()(lim0)(1lim0)(lim000???????????xxbxxxxxxxx????確定，之值，使，并在確定好，后求極限abxxaxbabxxxaxbxxlim()lim()???????????????3470347

6、22求極限lim()xxxxx?????11求極限limcossinxxxxx????23求極限lim()()()()()()xxxxxxx????????????121311011011112222???求極限lim()xxxxx???????2251求極限lim()xxxx???????485212討論極限limxxxxxeeee??????2343232求極限lim()()()()()()()xxxxxxxx?????????12

7、1314151233232求極限lim()()()()()()xxxxxxx?????????12131415153222222222335求極限lim()()()xxxx?????43326723425求極限，lim()xxxaaaa??????1012求極限limtantan()xxx?????424為無窮小時(shí)，之值，使當(dāng)，確定)(54)(2baxxxxfxba????????求極限limxxxxx?????1343243求極限li