Limits, Continuity and Differentiability

In this post, we shall discuss the importance of Limits, Continuity and Differentiability as a topic of preparation for JEE Advanced and JEE Mains. The important topics and the nature of problems shall also be discussed.

Importance

Yearly Trend

Limits, Continuity and Differentiability is a topic which is taught just after functions and provides some of the very essential tools to solve a variety of questions. So this chapter needs thorough practice and strong conceptual knowledge, for scoring of maximum possible marks in all the topics.

The trends from the previous years’ question papers show that the number of questions asked each year from this chapter varies a lot from as less as 1 question to as many as 4 questions.

The important topics shall be discussed next.

Topics

Unlike Functions, direct questions can be, and are asked from this chapter very frequently, so the grip over the concepts of this chapter should be strong, and that would come through enough practice.

The most important topic is Continuity and Differentiability conditions of a given function in a specified interval. The conditions those are necessary to prove the continuity and differentiability should be familiarised with very well. Second most important topics is Limits, especially the L-Hospital rule. Direct values of limits of a given function are often asked. These values may be finite or infinite in nature, which can be asked in the solution. Limits may be required to calculate for functions inside an integral. The concept of Inverse of a function is also really important. Questions will also be asked where expansions of standard functions will come in real handy, so learning them will be really helpful.

Problems for these chapters are also combined with other topics for formulation. These topics include Definite Integration, Application of Derivative etc.

This chapter then, can get you a lot of marks once the basics are cleared and enough questions are practiced.