题目

已知函数f(x)＝a－. (1)求证：函数y＝f(x)在(0，＋∞)上是增函数； (2)若f(x)<2x在(1，＋∞)上恒成立，求实数a的取值范围． 答案：解：(1)证明：当x∈(0，＋∞)时， f(x)＝a－， 设0<x1<x2，则x1x2>0，x2－x1>0. f(x1)－f(x2)＝ ＝<0. ∴f(x1)<f(x2)，即f(x)在(0，＋∞)上是增函数． (2)由题意a－<2x在(1，＋∞)上恒成立，设h(x)＝2x＋，则a<h(x)在(1，＋∞)上恒成立． 可证h(x)在(1，＋∞)上单调递增． 故a≤h(1)，即a≤3， ∴a的取值范围为听下面对话。对话后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。听每段对话前，你将有时间阅读各个小题，每小题5秒钟。听完后，每小题将给出5秒钟的作答时间。每段对话读两遍。 1．How long will it take them to get to Oldfield by car?     A. About a day.     B. About an hour.     C. About two and a half hours. 2．Why do they choose to take a picnic?     A. Because there are no restaurants in the park.     B. Because the restaurants there are expensive.     C. Because they prefer their own food and drinks. 3．Where have they finally decided to go?     A. Oldfield Adventure Park.     B. Newport Waterworld.     C. A small zoo.