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1、授课提示：对应学生用书第281 页A 组基础保分练 1.已知函数f(x)axln x(a0).(1)求 f(x)的单调区间；(2)试求 f(x)的零点个数，并证明你的结论.解析：(1)函数 f(x)的定义域是(0，)，f(x)(x)ln xx1xx（ln x2）2x.令 f(x)0，解得 xe2，令 f(x)0，解得 0 xe2，所以 f(x)在(0，e2)上单调递减，在(e2，)上单调递增.(2)由(1)得 f(x)minf(e 2)a2e，显然当 a2e时，f(x)min0，f(x)无零点，当 a2e时，f(x)min0，f(x)有 1 个零点，当 a2e时，f(x)min0，f(x)有
2、2 个零点.2.已知函数f(x)2ln(x1)(x1)2.(1)求函数 f(x)的单调递增区间；(2)若关于 x 的方程 f(x)x23x a0 在区间 2，4 内恰有两个相异的实根，求实数 a 的取值范围.解析：(1)由题意得函数f(x)的定义域是(1，)，f(x)21x1（x1）2x（x2）x1，x1，令 f(x)0，解得 1 x2，所以函数f(x)的单调递增区间是(1，2).(2)由 f(x)x2 3xa 0，得 xa12ln(x1)0，精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 1 页，共 5 页令 g(x)xa1 2ln(x1)，则 g(x)12x1x3x1(x
3、1)，由 g(x)0，得 x3，由 g(x)0，得 1x3，所以函数g(x)在2，3)上单调递减，在3，4上单调递增，作出函数g(x)在区间 2，4上的大致图像(图略)，可知方程f(x)x23x a0 在区间 2，4上恰有两个相异的实根，则g（2）0，g（3）0，g（4）0，即a30，a42ln 2 0，a52ln 3 0，解得 2ln 35a2ln 24，所以实数a 的取值范围是 2ln 3 5，2ln 24).B 组能力提升练 1.已知函数f(x)2ln xax2.(1)若 a 1，证明：f(x)10；(2)当 a1e时，判断函数f(x)有几个零点.解析：(1)证明：当a1 时，f(x)2
4、ln xx2，x(0，).f(x)2x2x2（1x2）x2（1x）（1 x）x.当 x 变化时，函数f(x)，f(x)变化情况如下表所示：(0，1)1(1，)f(x)0f(x)极大值 f(x)在 x1 处取得极大值，也是最大值，函数 f(x)的最大值为1，即当 x(0，)时，f(x)1，x(0，)时，f(x)10.(2)当 a1e时，f(x)2ln x1ex2，x(0，).精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 2 页，共 5 页文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2
5、A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M
6、2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3
7、M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W
8、3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9
9、W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O
10、9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6
11、O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3 f(x)2x2ex2（ex2）ex2（e x）（ex）ex.当 x 变化时，函数f(x)，f(x)变化情况如下表所示：(0，e)e(e，)f(x)0f(x)极大值 f(x)在 xe处取得极大值，也是最大值.f(
12、e)2lne1e(e)20，函数 f(x)在(0，)上只有一个零点.当 a1e时，函数 f(x)在(0，)上只有一个零点.2.已知函数f(x)xexa(ln xx)，aR.(1)当 a e时，求 f(x)的单调区间；(2)若 f(x)有两个零点，求实数a 的取值范围.解析：(1)由题意得，函数f(x)的定义域为(0，)，当 ae 时，f(x)xexeln x ex，则 f(x)（1x）（xexe）x.所以函数f(x)在(0，1)上单调递减，在(1，)上单调递增.(2)记 tln xx，则 tln xx 在(0，)上单调递增，且tR.所以 f(x)xexa(ln xx)etatg(t).所以 f
13、(x)在 x0 上有两个零点等价于g(t)etat 在 tR 上有两个零点.当 a0 时，g(t)et在 R 上单调递增，且g(t)0，故 g(t)无零点.当 a0 时，g(t)etat 在 R 上单调递增，又g(0)10，g1ae1a10，故 g(t)在 R 上只有一个零点.当 a0 时，由 g(t)eta0 可知 g(t)在 tln a 时有唯一的一个极小值g(ln a)a(1ln a).若 0ae，g(t)min a(1ln a)0，g(t)无零点；若 ae，g(t)min0，g(t)只有一个零点；若 ae 时，g(t)mina(1ln a)0，而 g(0)10，由于 h(x)ln xx
14、在 xe 时为减函数，可知ae时，eaaea2.从而 g(a)eaa20，所以 g(t)在(0，ln a)和(ln a，)上各有一个零点.精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 3 页，共 5 页文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7
15、 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I
16、7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4
17、I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z
18、4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2
19、Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E
20、2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6
21、E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3综上可知，a e时 f(x)有两个零点，即实数a 的取值范围是(e，).C 组创新应用练 已知函数f(x)12x2(1a)xaln x，aR.(1)若 f(x)存在极值点为1，求 a 的值；(2)若 f(x)存在两个不同的零点x1，x2，求证：x1 x2 2.解析：(1)由已知得f(x)x1aax，因为 f(x)存在极值点为1，所以 f(1)0，即 22a0，a1，经检验符合题意，所以a1.(2)证明：f(x)x 1aax(x1)1ax(x0)，
22、当 a0 时，f(x)0 恒成立，所以f(x)在(0，)上为增函数，不符合题意；当 a0 时，由 f(x)0 得 xa，当 xa 时，f(x)0，所以 f(x)单调递增，当 0 xa 时，f(x)0，所以 f(x)单调递减，所以当 xa 时，f(x)取得极小值f(a).又 f(x)存在两个不同的零点x1，x2，所以 f(a)0，即12a2(1a)a aln a0，整理得 ln a 112a，作 yf(x)关于直线x a 的对称曲线g(x)f(2ax)，令 h(x)g(x)f(x)f(2ax)f(x)2a2xaln2axx，则 h(x)22a2（2ax）x 22a2（xa）2a2 0，所以 h(
23、x)在(0，2a)上单调递增，不妨设 x1a x2，则 h(x2)h(a)0，即 g(x2)f(2ax2)f(x2)f(x1)，又 2ax2(0，a)，x1(0，a)，且 f(x)在(0，a)上为减函数，所以2ax2x1，即 x1x22a，精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 4 页，共 5 页文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10
24、N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ1
25、0N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ
26、10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:C
27、Z10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:
28、CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码
29、:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编
30、码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3又 ln a112a，易知 a1 成立，故 x1x2 2.精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 5 页，共 5 页文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7
31、 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I
32、7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4
33、I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z
34、4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2
35、Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E
36、2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3文档编码:CZ10N6E2Z4I7 HQ6O9W3M2A2 ZT2R5V10J10G3