The limit of function，which brings out the definitions of continuous function，derivative，definite integral，is the basis of“Higher Mathematics”. Thus，solving the limit of function is a very important problem. Firstly，we will introduce the common methods for solving the limit of function（sequence）in this paper. Secondly， we will give some examples to analysis the problems wihich should be paid attention to. Finally，we will obtain a brief description on the application of limit in other chapters of“Higher Mathematics”.