Why Asymptotic Behaviour of Limits is Important for Students to Learn before Differentiation ?

This paper explores how limits can be taught in an intuitive and meaningful way. Understanding the asymptotic behaviour of limits is a fundamental step in preparing students for differentiation in calculus. Limits describe how functions behave as inputs approach specific values or infinity, offering insight into long-term trends that are essential for grasping rates of change [1][2].Before learning differentiation, students must understand how functions grow, decay, or stabilize, as these behaviours directly influence core calculus ideas such as continuity, slopes, and instantaneous rates of change [25]. Without this foundational understanding, the process of differentiation can feel abstract and disconnected from real-world applications [27].Moreover, asymptotic analysis helps distinguish between functions that grow at different rates—such as exponential, logarithmic, and polynomial functions—which is essential for interpreting derivatives effectively [25][26].