吉林省延吉市金牌教育中心高中数学第三章不等式基础训练C组新人教A版必修51.若方程05)2(2mxmx只有正根,则m的取值范围是().A.4m或4mB.45mC.45mD.25m2.若aaxxxf12lg)(2在区间]1,(上递减,则a范围为()A.[1,2)B.[1,2]C.1,D.[2,)3.不等式22lglgxx的解集是()A.1(,1)100B.(100,)C.1(,1)100(100,)D.(0,1)(100,)4.若不等式2log0axx在1(0,)2内恒成立,则a的取值范围是()A.1116aB.1116aC.1016aD.1016a5.若不等式201xaxa有唯一解,则a的取值为()A.0B.21C.4D.66.不等式组131yxyx的区域面积是()A.12B.32C.52D.1二、填空题1.不等式122log(21)log(22)2xx的解集是_______________。2.已知0,0,1abab,则12a21b的范围是____________。3.若0,2yx且tan3tan,xy则xy的最大值为________.4.设0x,则函数1)1(2xxy在x=________时,有最小值__________。5.不等式24x0xx的解集是________________。三、解答题1.若函数()log(4)(0,1)aafxxaax且的值域为R,求实数a的取值范围。2.已知△ABC的三边长是,,abc,且m为正数,求证:abcambmcm。3.解不等式:3)61(log2xx24.已知求函数22()()()(02)xxfxeaeaa的最小值。设函数1)(2xbaxxf的值域为4,1,求ba,的值。参考答案(数学5必修)第三章[提高训练C组]一、选择题1.B21212(2)4(5)0(2)0,5450mmxxmmxxm2.A令221,,1uxaxa是的递减区间,得1a而0u须恒成立,∴min20ua,即2a,∴12a;3.D22lglg,lg2lg0,100,01xxxxxx或或4.A2logaxx在1(0,)2x恒成立,得01a,则2maxmin1111log,(log)log142416aaaxxxa。(另可画图做)5.B当20xaxa仅有一实数根,240,04aaaa或,代入检验,不成立或21xaxa仅有一实数根,2440,2aaa,代入检验,成立!33.62tantan2tan223tan()11tantan13tan3233tantanxyyxyxyyyy而0,022yxxy,3tan()36xyxy4.3,122111122()4()13xxxyxxxxx或5.2,00,3当0x时24x10,得02x;当0x时241x0,得30x;3,00,2x三、解答题解:令4auxx,则u须取遍所有的正实数,即min0u,而min24240041uaaaa且(0,1)1,4a证明:设()(0)xfxmxm,易知(0,)是()fx的递增区间,()()abcfabfc,即abcabmcm而abababambmabmabmabm4abcambmcm解:121068,,16xxxxxx当0x时,112,21xxxxx;当0x时,162,223223xxx(322,322)1x4.解:22222()2()2()2()22xxxxxxxxfxeeaeeaeeaeea令(2),()xxeettyfx,则22222ytata对称轴(02)taa,而2t2,是y的递增区间,当2t时,2min2(1)ya2min()2(1)fxa。5.解:令222,,0,1axbyyxyaxbyxaxybx显然0y可以成立,当0y时,2224()0,440ayybybya而14y,1和4是方程22440ybya的两个实数根所以214,144,34abab。5