题目

Two weeks before Christmas one year, I went to London with my   1  . I shall never forget the day. The streets were full of people. The shop windows were very bright. My mother held my hand and we both went into a 2   shop. The shop was full of   3  . There were nice toys   4  . Then I saw Father Christmas himself! I pulled my mother by   5  . “Please   6   me to Father Christmas,” I said. There were a lot of children near 7  . They were standing   8  . Father Christmas spoke to every one of them. At last it was my   9  . “Hello, little Tom,” he said t已知函数f（x）=lnx．（1）求函数g（x）=f（x+1）-x的最大值；（2）若对任意x＞0，不等式f（x）≤ax≤x2+1恒成立，求实数a的取值范围；（3）若x1＞x2＞0，求证：f(x1)-f(x2)x1-x2＞2x2x21+x22．