# Limits, Continuity and Differentiability

This chapter is divided into six sections.The first section deals with the introduction to limits which forms the basis of calculus.The evaluation of limits by direct substitution,factorization, rationalization and reductions to standard forms are discussed in the second section.Introduction to continuity is dealt in the third section.Differentiability and the concepts of left and right derivatives are discussed in the fourth section.Once we have the knowledge of continuity and differentiability, we can develop the applications of these concepts.The fifth sections deals with differentiation which is just an extension of the differentiability concept. In this section, we learn about the differentiation of standard functions, rules of differentiation, L'Hospital's Rule and so on.At the end of this section, we have a series of exercises to test your understanding of this chapter,solved examples, previous years’ IIT JEE questions pertaining to this chapter.

In addition to preparing for the JEE mains and advanced exams, Cuemath Founder Manan Khurma's study material is helpful for students who are appearing for CBSE, ICSE and other State board exams.

## Limits

- Introduction To Limits
- Left Hand and Right Hand Limits
- Introduction To Evaluating Limits
- Some Standard Limits
- Techniques of Evaluating Limits
- Examples on Evaluating Limits Set 1
- Examples on Evaluating Limits Set 2
- Examples on Evaluating Limits Set 3
- Examples on Evaluating Limits Set 4

## Continuity

- Introduction To Continuity
- Examples on Continuity Set 1
- Examples on Continuity Set 2
- Examples on Continuity Set 3
- Examples on Continuity Set 4

## Differentiability

- Introduction To Differentiability
- Left Hand and Right Hand Derivatives
- Differentiability of Some Basic Functions
- Examples on Differentiability Set 1
- Examples on Differentiability Set 2
- Examples on Differentiability Set 3

## Differentiation

- Introduction To Differentiation
- Differentiation of Polynomial and Trigonometric Functions
- Differentiation of Exponential Logarithmic and Inverse Trignometric Functions
- Rules of Differentiation
- Examples on Differentiation Set 1
- Differentiation of Parametric and Implicit Functions
- Examples on Differentiation Set 2
- L Hospital Rule

## Limits, Continuity and Differentiability