Limits, Continuity & Differentiability (Class 11–12) – JEE & CBSE by Meenakshi Shivhare

The Limits, Continuity & Differentiability course by Meenakshi Shivhare is a focused, concept-driven online Mathematics program designed for Class 11 and early Class 12 students, as well as aspirants preparing for JEE Main, IIT JEE, CBSE Applied Mathematics, and A & AS Level Mathematics. This topic forms the foundation of Calculus, and mastering it is essential for success in higher mathematics, physics, and competitive exams.

The course emphasizes conceptual clarity, step-by-step logic, and exam-oriented problem-solving, helping students move confidently from basic definitions to advanced applications. Whether you are encountering calculus for the first time or revising for entrance exams, this course builds accuracy, confidence, and mathematical maturity.

What Students Will Learn

📘 Limits

Concept of a limit and intuitive understanding

• Left-hand and right-hand limits

• Limits of algebraic, rational, trigonometric, and exponential functions

• Standard limits and their applications

• Limits at infinity and infinite limits
  Outcome: Students develop a clear understanding of how functions behave near a point—crucial for calculus-based problem solving.

📘 Continuity

Continuity of a function at a point

• Algebra of continuous functions

• Continuity of polynomial, rational, trigonometric, exponential, and logarithmic functions

• Continuity in graphical interpretation
  Outcome: Learners confidently analyze whether functions are continuous and apply concepts to both board-level and JEE questions.

📘 Differentiability

Differentiability at a point

• Relationship between continuity and differentiability

• Differentiability of standard functions

• Differentiability using first principles (introductory)

• Common non-differentiable functions and exam traps
  Outcome: Students gain a strong base for derivatives, avoiding common conceptual mistakes tested in exams.

📘 Exam-Oriented Applications

CBSE and JEE Main-style MCQs

• Concept-based subjective questions

• Graph-based and assertion–reason questions

• Problem-solving techniques and shortcut identification
  Outcome: Improved accuracy, speed, and confidence in competitive exam settings.

Teaching Method

Concept-First Teaching: Every idea is explained logically before formulas are applied.

• Step-by-Step Problem Solving: Problems are broken down into clear, manageable steps.

• Visual & Graph-Based Explanation: Helps students understand abstract concepts intuitively.

• Exam Pattern Alignment: Clear distinction between board-level and JEE-level expectations.

• Interactive Online Sessions: Students are encouraged to ask questions and clarify doubts in real time.

• Practice-Focused Learning: Regular problem sets to reinforce concepts and build confidence.

Why Learn from Meenakshi Shivhare?

Strong expertise in senior secondary and competitive Mathematics

• Clear, student-friendly explanation style for complex calculus concepts

• Focus on logic, accuracy, and conceptual depth rather than rote learning

• Balanced approach for CBSE, JEE Main, Applied Maths, and A & AS Level syllabi

• Supportive guidance to help students overcome fear of calculus

Who Should Join This Course?

Class 11 students starting Calculus

• Class 12 students revising core calculus foundations

• JEE Main / IIT JEE aspirants strengthening weak areas

• Students of CBSE Applied Mathematics

• A & AS Level Mathematics learners seeking concept clarity

Benefits & Outcomes

By the end of the course, students will:

• Clearly understand limits, continuity, and differentiability

• Avoid common conceptual and exam-related mistakes

• Solve board and JEE-level questions confidently

• Build a strong base for Derivatives, Applications of Derivatives, and Integrals

• Develop logical thinking and mathematical confidence