函数极限求解之依型定法探究
Research on the Method of Solving the Limit of Function Based on the Type

函数极限是大学数学中的重要概念，在函数的连续性、可导性和可积性等知识中都有重要应用。然而，函数极限的题目类型多样，求解方法繁多，学习难度较大。将常见的函数极限求解题型归纳为七种类型，即$C$ 型、$\frac{C}{0}$ 型、$\frac{0}{0}$ 型、$\frac{\infty }{\infty }$ 型、$\frac{C}{0}\pm \frac{C}{0}$ 型、含三角函数的$\frac{0}{0}$ 型及$1^{\infty }$ 型，并提出了一种判断类型，依型定法的函数极限求解策略可以根据函数类型，快速匹配每一种函数极限类型最佳的求解方法，从而实现函数极限的快速求解。
The limit of function is an important concept in the university mathematics, which has important applications in the knowledge of continuity, derivability and integrability of functions. However, it is very difficult to grasp the limit of function, because there are so many different types of functional limit problems and so many methods to solve them. The common question types of the limit of function are summarized into seven types: $C$ type, $\frac{C}{0}$ type, $\frac{0}{0}$ type, $\frac{\infty }{\infty }$ type, $\frac{C}{0}\pm \frac{C}{0}$ type, $\frac{0}{0}$ type involving trigonometric functions, and $1^{\infty }$ type. A