Ê®Äê¸ß¿¼ÕæÌâ·ÖÀà»ã±à(2010-2019) Êýѧ רÌâ04 µ¼ÊýÓ붨»ý·Ö ÎÞ´ð°¸Ô­¾í°æ ÏÂÔر¾ÎÄ

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(1)ÊÔÌÖÂÛf(x)µÄµ¥µ÷ÐÔ;

(2)Èôb=c-a(ʵÊýcÊÇÓëaÎ޹صij£Êý),µ±º¯Êýf(x)ÓÐÈý¸ö²»Í¬µÄÁã

µãʱ,aµÄÈ¡Öµ·¶Î§Ç¡ºÃÊÇ(-¡Þ,-3)¡È,ÇócµÄÖµ.

97.(2015¡¤±±¾©¡¤ÎÄT19)É躯Êýf(x)=-kln x,k>0. (1)Çóf(x)µÄµ¥µ÷Çø¼äºÍ¼«Öµ;

(2)Ö¤Ã÷:Èôf(x)´æÔÚÁãµã,Ôòf(x)ÔÚÇø¼ä(1,

2

]ÉϽöÓÐÒ»¸öÁãµã.

98.(2015¡¤Õã½­¡¤ÎÄT20)É躯Êýf(x)=x+ax+b(a,b¡ÊR).

(1)µ±b=+1ʱ,Çóº¯Êýf(x)ÔÚ[-1,1]ÉϵÄ×îСֵg(a)µÄ±í´ïʽ; (2)ÒÑÖªº¯Êýf(x)ÔÚ[-1,1]ÉÏ´æÔÚÁãµã,0¡Üb-2a¡Ü1.ÇóbµÄÈ¡Öµ·¶Î§.

99.(2014¡¤È«¹ú2¡¤ÎÄT21)ÒÑÖªº¯Êýf(x)=x-3x+ax+2,ÇúÏßy=f(x)ÔÚµã(0,2)´¦µÄÇÐÏßÓëxÖá½»µãµÄºá×ø±êΪ-2. (1)Çóa;

(2)Ö¤Ã÷:µ±k<1ʱ,ÇúÏßy=f(x)ÓëÖ±Ïßy=kx-2Ö»ÓÐÒ»¸ö½»µã. 100.(2014¡¤È«¹ú2¡¤ÀíT21)ÒÑÖªº¯Êýf(x)=e-e-2x. (1)ÌÖÂÛf(x)µÄµ¥µ÷ÐÔ;

(2)Éèg(x)=f(2x)-4bf(x),µ±x>0ʱ,g(x)>0,ÇóbµÄ×î´óÖµ; (3)ÒÑÖª1.414 2<

<1.414 3,¹À¼Æln 2µÄ½üËÆÖµ(¾«È·µ½0.001).

x

-x3

2

101.(2014¡¤È«¹ú1¡¤ÎÄT21)É躯Êýf(x)=aln x+0. (1)Çób;

x-bx(a¡Ù1),ÇúÏßy=f(x)ÔÚµã(1,f(1))´¦µÄÇÐÏßбÂÊΪ

2

(2)Èô´æÔÚx0¡Ý1,ʹµÃf(x0)<,ÇóaµÄÈ¡Öµ·¶Î§.

102.(2014¡¤È«¹ú1¡¤ÀíT21)É躯Êýf(x)=aeln x+y=e(x-1)+2.

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x

,ÇúÏßy=f(x)ÔÚµã(1,f(1))´¦µÄÇÐÏß·½³ÌΪ

13

Ãûʦ¾«ÐÄÕûÀí ÖúÄúÒ»±ÛÖ®Á¦

(1)Çóa,b; (2)Ö¤Ã÷:f(x)>1.

103.(2013¡¤È«¹ú2¡¤ÀíT21)ÒÑÖªº¯Êýf(x)=e-ln(x+m). (1)Éèx=0ÊÇf(x)µÄ¼«Öµµã,Çóm,²¢ÌÖÂÛf(x)µÄµ¥µ÷ÐÔ; (2)µ±m¡Ü2ʱ,Ö¤Ã÷f(x)>0.

104.(2013¡¤È«¹ú2¡¤ÎÄT21)ÒÑÖªº¯Êýf(x)=xe. (1)Çóf(x)µÄ¼«Ð¡ÖµºÍ¼«´óÖµ;

(2)µ±ÇúÏßy=f(x)µÄÇÐÏßlµÄбÂÊΪ¸ºÊýʱ,ÇólÔÚxÖáÉϽؾàµÄÈ¡Öµ·¶Î§.

105.(2013¡¤ÖØÇ졤ÎÄT20)ij´åׯÄâÐÞ½¨Ò»¸öÎ޸ǵÄÔ²ÖùÐÎÐîË®³Ø(²»¼Æºñ¶È).Éè¸ÃÐîË®³ØµÄµ×Ãæ°ë¾¶ÎªrÃ×,¸ßΪhÃ×,Ìå»ýΪVÁ¢·½Ã×.¼ÙÉ轨Ôì³É±¾½öÓë±íÃæ»ýÓйØ,²àÃæµÄ½¨Ôì³É±¾Îª100Ôª/ƽ·½Ã×,µ×ÃæµÄ½¨Ôì³É±¾Îª160Ôª/ƽ·½Ã×,¸ÃÐîË®³ØµÄ×ܽ¨Ôì³É±¾Îª12000¦ÐÔª(¦ÐΪԲÖÜÂÊ). (1)½«V±íʾ³ÉrµÄº¯ÊýV(r),²¢Çó¸Ãº¯ÊýµÄ¶¨ÒåÓò;

(2)ÌÖÂÛº¯ÊýV(r)µÄµ¥µ÷ÐÔ,²¢È·¶¨rºÍhΪºÎֵʱ¸ÃÐîË®³ØµÄÌå»ý×î´ó.

106.(2013¡¤È«¹ú1¡¤ÀíT21)É躯Êýf(x)=x+ax+b,g(x)=e(cx+d).ÈôÇúÏßy=f(x)ºÍÇúÏßy=g(x)¶¼¹ýµãP(0,2),ÇÒÔÚµãP´¦ÓÐÏàͬµÄÇÐÏßy=4x+2. (1)Çóa,b,c,dµÄÖµ;

(2)Èôx¡Ý-2ʱ,f(x)¡Ükg(x),ÇókµÄÈ¡Öµ·¶Î§.

107.(2013¡¤È«¹ú1¡¤ÎÄT20)ÒÑÖªº¯Êýf(x)=e(ax+b)-x-4x,ÇúÏßy=f(x)ÔÚµã(0,f(0))´¦µÄÇÐÏß·½³ÌΪy=4x+4. (1)Çóa,bµÄÖµ;

(2)ÌÖÂÛf(x)µÄµ¥µ÷ÐÔ,²¢Çóf(x)µÄ¼«´óÖµ.

x

2

2

x

2-xx

108.(2012¡¤È«¹ú¡¤ÀíT21)ÒÑÖªº¯Êýf(x)Âú×ãf(x)=f'(1)e-f(0)x+x. (1)Çóf(x)µÄ½âÎöʽ¼°µ¥µ÷Çø¼ä;

x-12

(2)Èôf(x)¡Ýx+ax+b,Çó(a+1)bµÄ×î´óÖµ. 109.(2012¡¤È«¹ú¡¤ÎÄT21)É躯Êýf(x)=e-ax-2. (1)Çóf(x)µÄµ¥µ÷Çø¼ä;

(2)Èôa=1,kΪÕûÊý,ÇÒµ±x>0ʱ,(x-k)f'(x)+x+1>0,ÇókµÄ×î´óÖµ. 110.(2012¡¤È«¹ú¡¤ÎÄT21)É躯Êýf(x)=e-ax-2.

Ãûʦ¾«ÐÄÕûÀí ÖúÄúÒ»±ÛÖ®Á¦

14

xx

2

Ãûʦ¾«ÐÄÕûÀí ÖúÄúÒ»±ÛÖ®Á¦

(1)Çóf(x)µÄµ¥µ÷Çø¼ä;

(2)Èôa=1,kΪÕûÊý,ÇÒµ±x>0ʱ,(x-k)f'(x)+x+1>0,ÇókµÄ×î´óÖµ.

111.(2011¡¤É½¶«¡¤ÀíT21)ijÆóÒµÄ⽨ÔìÈçͼËùʾµÄÈÝÆ÷(²»¼Æºñ¶È,³¤¶Èµ¥Î»:Ã×),ÆäÖÐÈÝÆ÷µÄÖмäΪԲÖù

ÐÎ,×óÓÒÁ½¶Ë¾ùΪ°ëÇòÐÎ,°´ÕÕÉè¼ÆÒªÇóÈÝÆ÷µÄÈÝ»ýΪÁ¢·½Ã×,ÇÒl¡Ý2r.¼ÙÉè¸ÃÈÝÆ÷µÄ½¨Ôì·ÑÓýöÓëÆä±í

Ãæ»ýÓйØ.ÒÑÖªÔ²ÖùÐβ¿·Öÿƽ·½Ã×½¨Ôì·ÑÓÃΪ3ǧԪ,°ëÇòÐβ¿·Öÿƽ·½Ã×½¨Ôì·ÑÓÃΪc(c>3)ǧԪ.Éè¸ÃÈÝÆ÷µÄ½¨Ôì·ÑÓÃΪyǧԪ.

(1)д³öy¹ØÓÚrµÄº¯Êý±í´ïʽ,²¢Çó¸Ãº¯ÊýµÄ¶¨ÒåÓò; (2)Çó¸ÃÈÝÆ÷µÄ½¨Ôì·ÑÓÃ×îСʱµÄr.

112.(2011¡¤È«¹ú¡¤ÀíT21)ÒÑÖªº¯Êýf(x)=(1)Çóa,bµÄÖµ;

,ÇúÏßy=f(x)ÔÚµã(1,f(1))´¦µÄÇÐÏß·½³ÌΪx+2y-3=0.

(2)Èç¹ûµ±x>0,ÇÒx¡Ù1ʱ,f(x)>,ÇókµÄÈ¡Öµ·¶Î§.

113.(2011¡¤È«¹ú¡¤ÎÄT21)ÒÑÖªº¯Êýf(x)=(1)Çóa,bµÄÖµ;

,ÇúÏßy=f(x)ÔÚµã(1,f(1))´¦µÄÇÐÏß·½³ÌΪx+2y-3=0.

(2)Ö¤Ã÷:µ±x>0,ÇÒx¡Ù1ʱ,f(x)>.

x

2

114.(2010¡¤È«¹ú¡¤ÀíT21)É躯Êýf(x)=e-1-x-ax. (1)Èôa=0,Çóf(x)µÄµ¥µ÷Çø¼ä;

(2)Èôµ±x¡Ý0ʱf(x)¡Ý0,ÇóaµÄÈ¡Öµ·¶Î§.

115.(2010¡¤È«¹ú¡¤ÎÄT21)É躯Êýf(x)=x(e-1)-ax.

x

2

(1)Èôa=>,Çóf(x)µÄµ¥µ÷Çø¼ä;

(2)Èôµ±x¡Ý0ʱf(x)¡Ý0,ÇóaµÄÈ¡Öµ·¶Î§.

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15