Understanding Limits in Calculus

Categories: Mathematics
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About Course

Course Overview:

This comprehensive course on “Understanding Limits in Calculus” is designed to provide class 12 students, particularly those preparing for the IIT JEE and other competitive exams, with a strong foundation in the fundamental concept of limits. Limits are a crucial topic in calculus and serve as the building blocks for more advanced concepts such as derivatives and integrals.

Course Objectives:


  1. Conceptual Understanding: Develop a deep and intuitive understanding of limits, their significance, and how they are applied in calculus.


  1. Problem Solving Skills: Equip students with the skills and techniques needed to solve a wide range of limit problems, including indeterminate forms, using various approaches.


  1. Applications in Physics and Engineering: Explore practical applications of limits in real-world scenarios, especially in the context of physics and engineering problems.


  1. Preparation for Competitive Exams: Provide a solid foundation in limits to help students excel in their class 12 board exams and competitive exams like IIT JEE.

By the end of this course, students will have a solid grasp of limits, enabling them to confidently tackle more advanced topics in calculus and excel in their class 12 exams and competitive entrance tests like the IIT JEE.

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What Will You Learn?

  • Definition of a Limit: You will understand the formal definition of a limit, which is the core concept of this chapter.
  • Limit Notation and Terminology: You will become familiar with limit notation, including the use of symbols such as "lim" and "→," and learn how to interpret and use this notation effectively.
  • One-Sided Limits: You will explore the concept of one-sided limits, which help determine if a function approaches a specific value from the left or right side.
  • Basic Limit Properties: You will learn essential properties of limits, such as the sum, difference, product, and quotient properties, which are crucial for evaluating limits of functions.
  • Evaluating Limits: You will develop skills in evaluating limits using various techniques, including direct substitution, factoring, simplification, and rationalisation.
  • Special Limits: You will tackle limits involving trigonometric functions, exponential functions, and logarithmic functions, which often appear in calculus problems.
  • Techniques for Solving Limit Problems: You will acquire problem-solving techniques, including L'Hôpital's Rule and the Squeeze Theorem, which help evaluate limits in complex cases.

Course Content

Introduction to Limits
Understand the basics of Limits. You will learn the basic definitions and terminologies we will be using in the entire chapter.

  • Definition of Limit
  • Indeterminate Forms
  • Fundamental Properties

Methods of Evaluation
You will learn the various methods used to evaluate the Limits.

Different forms of Limits
You will learn the different special forms of limits like trigonometric limit, exponential limit and so on.

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