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Continuity and Differentiability — Important Topics

JEE Advanced · Mathematics

Most important topics from Continuity and Differentiability for JEE Advanced Mathematics 2026 — high-weightage areas based on previous year analysis.

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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.
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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.

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