2016?7???????????????

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?1? ??

?2? ?????

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?????????? C ??????????

2 A. f(x)?(x)?g(x)?x B. f(x)?x2?g(x)?x

x2?1 C. f(x)?lnx?g(x)?3lnxD. f(x)?x?1?g(x)? x?1

????f(x)?????(??,??)????f(x)?f(?x)??????C???? 3

A. ???? B. x?

C. y?D. y?x

???????????? B ??

A. y?ln(1?x)B. y?xcosx 2

ax?a?x

C. y?D. y?ln(1?x) 2

???????????????C??

A. y?x?1 B. y??x

C. y?x2 D. y????1,x?0 1,x?0?

?????????????? D ??

x2

?1B. limln(1?x)?0A. lim2x?0x??x?2

sinx1 C. lim?0 D. limxsin?0 x??x??xx

??x?0????? C ???????

1sinx A.B. xx

1 C. xsin D. ln(x?2) x

????f(x)??x0??? A ???f(x)??x0???

A. limf(x)?f(x0)B. f(x)??x0????????? x?x0

C. lim?f(x)?f(x0)D. lim?f(x)?lim?f(x) x?x0x?x0x?x0

??????

x2?9?ln(1?x)?????????f(x)?x?322 ?????f(x?1)?x?x??f(x)?

1x1/ 2 ?lim(1?? )?x??2x

1?x? ????f(x)??(1?x),x?0??x?0?????k? e?

?x?0?x?k,

?x?1,x?0 ???y??????? ? ?sinx,x?0

??limf(x)?A???x?x0??f(x)?A??? x?x0

??????

????

?ex,f(x)???x,

????y?lglgx?0x?0 ??f(?2),f(0),f(1)? ??f(-2) = - 2?f(0) = 0? f(1) = e 2x?1????? x

2x?1 ????0??x<0?x>1/2???????(-??0)?(1/2?+?) x

?????R??????????

????????????????????????A=(R+b)h???b? 22? R2?h2 A?(R?R?h)h

sin3x3sin3x?3lim?lim??x?0sin2xx?02sin2x22xx2?1x?1lim?lim(x?1)??2x??1sin(x?1)x??1sin(x?1)

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?? tan3xsin3xlim?lim3cos3x?3x?0x?0x3x?x2?1(?x2?1)(?x2?1)lim?limx?0x?0sinx(?x2?1)sinxx?lim?lim?022x?0x?0(?x?1)sinx?x?1sinxx?1xx?3?4x?4xlim()?lim()?lim(1?)x??x?3x??x??x?3x?3x?3(1?x2)?1x?4?4?4[(1?)]2x?6x?8(x?2)(x?4)2?e?4limlim? x?4x2?5x?4x?x?4(x?1)(x??4)33 (1?) ???? x?3?(x?2)2,x?1?f(x)??x,?1?x?1??f(x)??????????????

?x?1,x??1?

x?1 ?? x?1lim?f(x)?(1?2)2?1?lim?f(x)?1

limf(x)?1?f(1)x?1limf(x)??1?limf(x)??1?1?0x??1?x??1?????x=1???

x??1limf(x)

????????x=-1???? ???????????

?3? ?????

????????

f(x)f(x)????lim?? B ?? x?0x?0xx

A. f(0) B. f?(0)

C. f?(x) D. 0

f(x0?2h)?f(x0) ??f(x)?x0????lim??D?? h?02h

A. ?2f?(x0)B. f?(x0)

C. 2f?(x0) D. ?f?(x0)??f(0)?0???lim

f(1??x)?f(1)??A?? ?x?0?x

A. e B. 2e

11 C. eD. e 24

??f(x)?x(x?1)(x?2)?(x?99)??f?(0)??D????f(x)?e??limx

A. 99 B. ?99

C. 99!D. ?99!

??????????? C ??

A. ?f(x)??x0???????x0???

B. ?f(x)??x0??????x0???

C. ?f(x)??x0??????x0????

D. ?f(x)??x0???????x0???

??????

1?2?xsin,x?0 ????f(x)????f?(0)? x?x?0?0,

df(lnx)x2xx????f(e)?e?5e??dx

x?1?(1,2)??????? ?

? ???f(x)?sinx?(,1)??????? ? 42x2x ??y?x??y?????f(x)?

??y?xlnx??y????

??????

?????????y?? ?y?(xx?3)ex y=(x3/2+3)ex?y?=3/2x1/2ex+(x3/2+3)ex

=(3/2x1/2+x3/2+3)ex

?y?cotx?x2lnxy?=-csc2x + 2xlnx +x x2?y?y?=(2xlnx-x)/ln2x lnx

cosx?2xx32x6 ?y? y?=[(-sinx+2ln2)x-3x(cosx+2)]/xx3

?y?lnx?x= sinx2

?y?x4?sinxlnxy?=4x3-cosxlnx-sinx/x 1(?2x)sinx?(lnx?x2)cosxsin2x

sinx?x2x2x2x?y? y?=[(cosx+2x)3-(sinx+x)3ln3]/3 3x

=[cosx+2x-(sinx+x2)ln3]/3x

?y?extanx?lnx y?=extanx+exsec2x+1/x = ex(tanx+sec2x)+1/x ?????????y?? ?y?e?x

?y?lncosx32

?y?xxx y=x7/8 y?=(7/8)x -1/8 ?y?x?x

?y?cos2ex

?y?cosex

?y?sinnxcosnx y?=nsinn-1xcosxcosnx - nsinnxsin nx ?y?5sinx

?y?esinx

?y?xx?ex

?y?xe?ee

????????y?y(x)???????????y?? ?ycosx?e2y???x???y?cosx-ysinx=2 y?e2y 22222xx

y?=ysinx / (cosx-2e2y)

?y?cosylnx ???x???y ?= y ?(-siny)lnx +(1/x)cosy

y?=[(1/x)cosy] / (1+sinylnx) x2?2xsiny? ???x???2siny + y?2xcosy=(2xy-x2 y?)/y2 y

y?=2(xy �y2siny) /(x2+2xy2cosy)

?y?x?lny ???x???y?=1+ y?/y? y?=y /(y-1) ?lnx?ey?y2???x???1/x+ y?ey=2y y?? y?=1/x(2y-ey)

?y2?1?exsiny ???x???2y y?=exsiny + y? excosy

y?= exsiny/(2y- excosy)

?ey?ex?y3???x???y?ey =ex -3y2 y?? y?=ex/ey+3y2 ?y?5x?2y???x???y?=5xln5 + y?2yln2? y?=5xln5 /(1-2yln2) ?????????dy?

?y?cotx?cscx lnx sinx

1?x?y?arcsin 1?x

1?x?y? 1?x

?y?sin2ex ?y?

?y?tanex

????????????

?y?xlnx

?y?xsinx

?y?arctanx

?y?3x

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?f(x)??????????f?(x)?????

???? f(x)= - f(-x) ??f?(x)= - f?(-x)(-x)? f?(x)= f?(-x)? ?f?(x)????

23

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???2014??????????????????

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?1? ??

?2? ?????

??? ?????

??????????C ??????????

A. f(x)?(x)2?g(x)?x B. f(x)?x2?g(x)?x

x2?13 C. f(x)?lnx?g(x)?3lnxD. f(x)?x?1?g(x)? x?1

????f(x)?????(??,??)????f(x)?f(?x)??????C????

A. ???? B. x?

C. y?D. y?x

????????????B??

A. y?ln(1?x2)B. y?xcosx

ax?a?x

1?x)C. y?D. y?ln(2

???????????????C??

A. y?x?1 B. y??x

C. y?x2??1,x?0 D. y?? 1,x?0?

??????????????D??

x2

?1B. limln(1?x)?0A. lim2x?0x??x?2

sinx1?0 D. limxsin?0C. limx??x??xx

??x?0?????C???????

sinx1 A.B. xx

1 C. xsin D. ln(x?2) x

????f(x)??x0???A???f(x)??x0???

A. limf(x)?f(x0)B. f(x)??x0????????? x?x0

f(x)?f(x0)D. limf(x)?limf(x)C. lim???x?x0x?x0x?x0

?????? x2?9???f(x)??ln(1?x)??????x|x?3?x?322?????f(x?1)?x?x??f(x)? 1x)?? ?lim(1?x??2x

11x12x?1

lim(1?)?lim(1?)2?e2 x??x??2x2x

1?x?????f(x)??(1?x),x?0??x?0?????k? e?

?x?0?x?k,

?x?1,x?0???y???????x?0 sinx,x?0?

??limf(x)?A???x?x0??f(x)?A??x?x0??????? x?x0

??? ???

????

?ex,x?0f(x)?? ?x,x?0

??f(?2),f(0),f(1)?

??f??2???2?f?0??0?f?1??e?e 1

2x?1????? x

?2x?1??x?0??2x?11???y?lg??????????x??x?0 x2?x?0????x?0?1????????x|x?0?x?? 2??

?????R??????????????????????????????????????y?lg??????????????????????

??

A

O h

B

C

???ABCD?????????????h??OE=h???CD?2R

?????AOE?????????

AE?

????2AE?h2R??hR? 2

sin3x??lim? x?0sin2x?S???

sin3xsin3x?3xsin3x3133??lim?lim?lim???? x?0sin2xx?0x?02122?2x2x2x

x2?1??lim? x??1sin(x?1)

x2?1(x?1)(x?1)x?1?1?1?lim?lim???2 ??limx??1sin(x?1)x??1sin(x?1)x??11

x?1

tan3x??lim? x?0x

tan3xsin3x1sin3x11?lim?lim??3?

1??3?

3

??limx?0x?

0xxcos3xx?03xcos3x1

?x2?1

??lim? x?012

????limx?0x?0x?0sinx

?limx?0 x1)x?0?0 1?1?1??lim(x??x?1x)? x?3

111(1?)x[(1?)?x]?1x?1xe?1

x?4??lim( )?lim()?lim?lim??ex3x??x?3x??x??xx??e11?(1?)[(1?)3]3

xx3

x2?6x?8??lim2? x?4x?5x?4

x2?6x?8?x?4??x?2??limx?2?4?2?2 ??lim2?limx?4x?5x?4x?4x?4x?1x?4x?14?131?????

?(x?2)2,x?1?f(x)??x,?1?x?1

?x?1,x??1?

??f(x)??????????????

????????x??1,x?1??????

?1?

x??1?

x??1?limf?x??limx??1x??1?x??1?limf?x??lim?x?1???1?1?0

??limf?x??limf?x???f?x??x??1???? x??1?x??1?

?2?

x?1?

x?1?limf?x??lim?x?2???1?2??1x?1?x?1?22limf?x??limx?1

f?1??1

??limf?x??limf?x??f?1??f?x??x?1??? x?1?x?1?

??1??2??f?x????x??1????

?f?x??????????,?1?

?3? ?????

???????? ??1,??? ?????????????

f(x)f(x)??C ?? ????limx?0x?0xx

A. f(0) B. f?(0)

C. f?(x) D. 0cvx

f(x0?2h)?f(x0)??D ????f(x)?x0????limh?02h

A. ?2f?(x0)B. f?(x0)

C. 2f?(x0) D. ?f?(x0)??f(0)?0???lim

f(1??x)?f(1)??A ?? ?x?0?x

A. e B. 2e

11 C. eD. e 24

??f(x)?x(x?1)(x?2)?(x?99)??f?(0)??D ????f(x)?ex??lim

A. 99 B. ?99

C. 99!D. ?99!

??????????? C ??

A. ?f(x)??x0???????x0???

B. ?f(x)??x0??????x0???

C. ?f(x)??x0??????x0????

D. ?f(x)??x0???????x0???

??????

1?2?xsin,x?0 ????f(x)????f?(0)? x?x?0?0,

df(lnx)2lnx5? ??xxdx

1 ???f(x)?x?1?(1,2)???????k? 2

?22? ???f(x)?sinx?(,1)???????y?x?(1?) 4224

??y?x2x??y??2x2x(1?lnx)

1 ??y?xlnx??y??? x ??f(ex)?e2x?5ex??

??????

?????????y?? 3x?y?(xx?3)e y??(x?3)e?x2e 2

?y?cotx?x2lnx y???csc2x?x?2xlnx xx321

2xlnx?xx2

?y?y?? 2lnxlnx

cosx?2xx(?sinx?2xln2)?3(coxs?2x)?y? y?? 3xx4

1sinx(?2x)?(lnx?x2)cosx2lnx?x?y?y?? 2sinxsinx

sinx3?cosxlnx ?y?x4?sinxlnxy??4x?x

sinx?x23x(cosx?2x)?(sinx?x2)3xln3?y? y?? 32x3x

ex1xxx???y?etanx?lnx y??etan 2cosxx

?????????y?? ?y?e1?x2

?x

?y?lncosx3 y??e?x2x2

?sinx3

223y??3x??3xtanx 3cosx

?y?

7

8xxx ?17y?xy??x8 8?y?x?x

1?2?111y??(x?x2)3(1?x2) 32

2x?y?cose


?2016?7???????????????????????
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