Concepts of limits and continuity from "summary" of Differential Calculus by S Balachandra Rao
In the realm of calculus, the notions of limits and continuity play a pivotal role in understanding the behavior of functions. These concepts serve as the foundation upon which various calculus techniques are built, making them fundamental to the study of differential calculus.
The concept of limits can be thought of as a way to describe the behavior of a function as it approaches a certain value. When we talk about the limit of a function as x approaches a specific value, we are essentially examining the values that the function takes on as x gets closer and closer to that particular value. This notion of approaching a value without necessarily reaching it is crucial in calculus, as it allows us to analyze functions in a more nuanced manner.
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