This study takes the limit problems in high school and university physics teaching as the research object, analyzes typical cases, systematically compares the differences between the two stages in teaching objectives, concept introduction methods, cognitive requirements, and mathematical tools, reveals students' difficulties in transition, and proposes teaching strategies for high school and university teachers based on the concept change theory. This study is helpful to improve the teaching research of limit problems, promote students' transition between different stages, and provide theoretical basis and practical reference for front line teachers' teaching design and implementation.