Skip to main content
Super TutorResources
Chapter 19 of 42
SyllabusNotesTopicsQuestionsPlanFormulas
Syllabus

Continuity and Differentiability — Syllabus

JEE Advanced · Mathematics

Free Continuity and Differentiability syllabus for JEE Advanced Mathematics 2026 — topics covered, weightage, and preparation priorities for this chapter.

Interactive on Super Tutor

Studying Continuity and Differentiability? Get the full chapter — free.

Practice questions, revision notes, formula sheet and AI doubt-solver — built for JEE Advanced Mathematics.

Try Super Tutor — Free
A Cartesian coordinate system showing the step-like graph of the signum function, f(x) = -1 for x<0, 0 for x=0, and 1 for x>0.
Super Tutor

This is just one of 16+ visuals inside Super Tutor's Continuity and Differentiability chapter

Explore the full set

Continuity and Differentiability — Syllabus & Topics

Topics covered in Continuity and Differentiability for JEE Advanced Mathematics.

Topics in Continuity and Differentiability

1

Continuity of Functions

  • A function f(x) is continuous at x = a if lim(x→a) f(x) = f(a)
  • Three conditions for continuity: function is defined at the point, limit exists, and limit equals function value
  • Functions like polynomials, trigonometric, exponential, and logarithmic are continuous in their domains
2

Types of Discontinuities

  • Removable discontinuities: missing point or isolated point
  • Non-removable discontinuities: jump, infinite, or oscillatory type
  • Greatest integer function [x] has jump discontinuities at all integers
3

Differentiability

  • f'(a) = lim(h→0) [f(a+h) - f(a)]/h, provided limit exists and is finite
  • Left derivative f'(a⁻) and right derivative f'(a⁺) must be equal for differentiability
  • Differentiability implies continuity, but not vice versa
4

Continuity and Differentiability of Composite Functions

  • If f and g are continuous, then fog is continuous wherever defined
  • Chain rule: (fog)'(x) = f'(g(x)) · g'(x)
  • Composition can create or remove discontinuities

Key Concepts

A function f(x) is continuous atDiscontinuities are classified asIf f(x) is continuous on [aA function f(x) is differentiable atIf f(x) is differentiable at x

Frequently Asked Questions

What topics are covered in Continuity and Differentiability for JEE Advanced?
Continuity and Differentiability is an important chapter in JEE Advanced Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Continuity of Functions, Types of Discontinuities, Differentiability, Continuity and Differentiability of Composite Functions.
How important is Continuity and Differentiability for JEE Advanced?
Continuity and Differentiability is a frequently tested chapter in JEE Advanced Mathematics. Questions from this chapter appear regularly in previous year papers. There are 55 practice questions available for this chapter.
How to prepare Continuity and Differentiability for JEE Advanced?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

More resources for Continuity and Differentiability

All 42 chapters — JEE Advanced Mathematics Syllabus

For JEE Advanced aspirants

Get the full Continuity and Differentiability chapter — for free.

Practice questions, revision notes, formula sheet and AI doubt-solver for JEE Advanced Mathematics.

Try Super Tutor Free
Try the full chapter — Free