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1.试题内容已知函数f(x)=xlnx+ax+b在(1,f(1))处的切线为2x-2y-1=0.(Ⅰ)求f(x)的单调区间与最小值;(Ⅱ)证明:e~x+lnx>cosx+(sinx-1)/x.2.考查目标本小题主要考查导数公式和运算法则及其几何意义、函数的单调性、零点存在定理,不等式等基础知识,综合考查推理论证能力、运算求解能力等,以及函数与方程思想、化归与转化思想、分类与整合思想.3.命制过程命题者欲命制一道函数不等式问题作为理科压轴练习,故设想函数背景适当复杂,可含有指数函数、
1. Problem Description It is known that the tangent to f (x) = xlnx + ax + b at (1, f (1)) is 2x-2y-1 = Minimum value; (Ⅱ) Proof: e ~ x + lnx> cosx + (sinx-1) /x.2. Examination of the main purpose of this topic to examine the derivative formula and algorithm and its geometric meaning, monotonicity of the function, zero existence theorem , Inequality and other basic knowledge, a comprehensive examination of the ability of reasoning and argumentation, the ability to solve the operation, as well as the function and the idea of the equation, the idea of conversion and transformation, classification and integration.3.Positional process The propositional desire to function inequality as a subject Finale practice, it is assumed that the function background is appropriate and complex, may contain an exponential function,