极限思想在数学中占有举足轻重的地位,现行高中教材中有多处内容渗透了极限的思想和方法,如“球的体积和表面积”、“双曲线的渐近线”等,但是极限思想在实际教学中没有得到普遍的认可和重视,学生对这种思想方法相当陌生.下面笔者尝试将极限思想和方法渗透、融合在解题教学中,实现方法与内容的整合. The idea of ​​limit plays a very important role in mathematics. There are many contents in the current high school textbooks that permeate the limits of thought and method, such as “the volume and surface area of ​​the ball” and the “asymptote of the hyperbola”, but the ultimate thinking is practical. Teaching has not been universally recognized and valued. Students are quite unfamiliar with this method of thinking. The following author attempts to infiltrate and integrate the limit thoughts and methods in problem-solving teaching and realize the integration of methods and contents.