Limits are an important focus in the study of advanced mathematics,and it is an important foundation and theoreti-cal tool for students'subsequent learning.However,due to the diverse forms of limit problems,it is also a difficult point for students,especially the methods of solving indeterminate forms of limits are flexible and diverse.The commonly used methods for solving 0/0 tepyindeterminate limits are L'Hopital's rule and the substitution of equivalent infinitesimals,etc.In addition to L'Hopi-tal's rule,methods for solving ∞/∞ tepy indeterminate limits also include the use of important limits,the transformation between in-finity and infinitesimals,and important conclusions,etc.In this paper,for an exercise of ∞/∞ tepy indeterminate form limit,six solu-tions are given by using L'Hospital's rule and its combination with various forms of trigonometric identity transformation,and each solution is analyzed in detail.Finally,the conclusion is drawn to improve the students'calculation ability and divergent thinking.
Indeterminate form limitL'Hospital's ruleTrigonometric identity TransformationDivergent thinking
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