函数f(x)=lnx﹣的零点所在的大致区间是( ) A.(1,2) B.(2,

函数f(x)=lnx﹣的零点所在的大致区间是(  )

A.(1,2) B.(2,3) C.(1,) D.(e,+∞)

答案

B【考点】二分法求方程的近似解.

【专题】计算题;函数的性质及应用.

【分析】直接通过零点存在性定理,结合定义域选择适当的数据进行逐一验证,并逐步缩小从而获得最佳解答.

【解答】解:函数的定义域为:(0,+∞),有函数在定义域上是递增函数,所以函数只有唯一一个零点.

又∵f(2)﹣ln2﹣1<0,f(3)=ln3﹣>0

∴f(2)•f(3)<0,

∴函数f(x)=lnx﹣的零点所在的大致区间是(2,3).

故选:B.

【点评】本题考查的是零点存在的大致区间问题.在解答的过程当中充分体现了定义域优先的原则、函数零点存在性定理的知识以及问题转化的思想.值得同学们体会反思.

 

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