osx
11limxcot2x
x0
5
f12limx2ex2
x0
1
13lim221x1x1x114lim1axxx15limxsi
x
x0
16lim1ta
xx0x
1l
1xlim1xlim11解1limx0x01x01xx
xxxx2limeelimee2x0si
xx0cosx3limsi
xsi
alimcosxcosaxaxa1xa3x34limsi
3xlim3cosxta
5xx5sec25x5
5lim
x2
2l
si
xlimcotx1limcscx124x282xx22x222
mmm1m16limx
a
limmx
1mx
1mam
xaxaxa
x
a
1sec27x7l
ta
7x7limlimta
7xx0l
ta
2xx01sec22x2ta
2x
27limta
2x7limsec22x212x0ta
7x2x0sec7x7
8lim
x2
ta
xlimsec2x1limcos23xta
3xxsec23x33xcos2x
22
1lim3x
2
2cos3xsi
3x3limcos3x2cosxsi
xxcosx
2
lim3si
3x3xsi
x
2
111x2l
1112xx9limlimlim1x2xarccotxxxxx121x
6
flim2xlim21x12xx22l
1x2cosxl
1x2limlimx210lim2x0secxcosxx0x01cosx1cosx2xlimlimx1x02cosxsi
xx0si
x
注cosxl
1x2x211limxcot2xlim
x0
112limx2ex2x0
x
1
x0ta
2x
lim
x0sec22x2
1
12
ttx2limelimelimex01ttt1x2
注当x0时t1x221lim1xlim1113limx1x21x1x1x21x12x214因为lim1axlimexxx
xl
1ax
1aax2l
11axlimx1alim而limxl
xxxx112xx
limaxlimaaxxax1
所以lim1axlimexxx15因为limxsi
xlimesi
xl
x
x0x0
xl
1axea
1l
xxlim而limsi
xl
xlimx0x0cscxx0cscxcotx
2limsi
x0x0xcosx
所以limxsi
xlimesi
xl
xe01
x0x0
16因为lim1ta
xeta
xl
xx0x
7
f1l
xxlim而limta
xl
xlimx0x0cotxx0csc2x
2limsi
x0x0x所以lim1ta
xlimeta
xl
xe01x0xx0
r