Skip to main content
Super TutorResources
Chapter 8 of 13
Concept Maps

Continuity and Differentiability — Concept Maps

ICSE · Class 12 · Mathematics

4 concept maps of Continuity and Differentiability for ICSE Class 12 Mathematics, each also written out as a text outline.

105 questions29 flashcards9 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Continuity and Differentiability? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for concept maps and more.

Try Super Tutor — Free

Free trial, no card needed.

A graph of a continuous function at a specific point, showing the limit approaching the function value, illustrating that the function is unbroken and defined at that point.
Super Tutor

Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Continuity and Differentiability.

4 Concept Maps

Decision Tree: Is a Function Continuous at Point c?

Decision Tree: Is a Function Continuous at Point c?

The map in words

  • Is f(c) defined?
    • No: NOT Continuous (f(c) does not exist)
    • Yes: Does lim(x→c⁺) f(x) exist?
      • No: NOT Continuous (Right limit missing)
      • Yes: Does lim(x→c⁻) f(x) exist?
        • No: NOT Continuous (Left limit missing)
        • Yes: Are the limits equal? lim(x→c⁺) = lim(x→c⁻)
          • No: NOT Continuous (Jump discontinuity)
          • Yes: Does lim(x→c) f(x) = f(c)?
            • No: NOT Continuous (Removable discontinuity)
            • Yes: ✓ CONTINUOUS at x = c

Continuity and Differentiability - Complete Overview

Continuity and Differentiability - Complete Overview

The map in words

  • Continuity and Differentiability
    • Limits
      • Definition
      • Right-hand limit
      • Left-hand limit
      • Standard limits
      • Limit laws
    • Continuity at a Point
      • Three conditions
      • Left continuity
      • Right continuity
      • Discontinuity types
      • Removable discontinuity
      • Jump discontinuity
      • Infinite discontinuity
    • Continuity on Intervals
      • Open interval continuity
      • Closed interval continuity
      • Algebra of continuous functions
      • Composition of continuous functions
    • Differentiability at a Point
      • Derivative definition
      • Right derivative
      • Left derivative
      • Geometric interpretation
      • Non-differentiability reasons
      • Corner points
      • Cusps
      • Vertical tangents
    • Differentiability on Intervals
      • Open interval differentiability
      • Closed interval differentiability
      • Algebra of derivatives
      • Chain rule
      • Differentiability implies continuity
    • Key Theorems
      • Rolle's Theorem
      • Mean Value Theorem
      • Intermediate Value Theorem
      • Composition theorems
    • Problem Types
      • Finding constants
      • Checking continuity
      • Checking differentiability
      • Identifying discontinuities
      • Applying theorems

Flowchart showing how limits are determined by comparing left and right limits

Flowchart showing how limits are determined by comparing left and right limits

The map in words

  • Limit Concept
    • Right-Hand Limit lim x→c+ f(x)
      • Both limits equal?
        • Yes: Limit Exists lim x→c f(x) = L
        • No: Limit Does Not Exist
    • Left-Hand Limit lim x→c- f(x)

Continuity and Differentiability of real functions

Continuity and Differentiability of real functions

The map in words

  • Continuity and Differentiability of real functions
    • Limits
    • Continuity at a point
    • Discontinuity at a point
    • Continuity on an interval
    • Algebra of continuous functions
    • Examples of continuous functions
    • Greatest integer function and fractional part type function
    • Differentiability at a point

Explore these maps interactively

Explore Diagrams

Frequently Asked Questions

What are the important topics in Continuity and Differentiability for ICSE Class 12 Mathematics?
Key topics in Continuity and Differentiability include Limits and One-Sided Limits, Continuity at a Point and on an Interval, Algebra of Continuous Functions, Differentiability at a Point and One-Sided Derivatives. Study these first, then practise questions on each for the ICSE Class 12 board exam.
What do the concept maps for Continuity and Differentiability show?
The 4 maps show how the ideas in Continuity and Differentiability connect: Decision Tree: Is a Function Continuous at Point c?; Continuity and Differentiability - Complete Overview. Each map is also written out as an outline on this page.
How should I revise Continuity and Differentiability for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 105 practice questions on Continuity and Differentiability. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Continuity and Differentiability

All ICSE Class 12 Mathematics Concept Maps

For serious students

Get the full Continuity and Differentiability chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for ICSE Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free