Chapter 7 · Class 11-12 & JEE Main/Adv
Continuity & Differentiability
41 topics in 15 parts
Power rule (derivative) Continuity at a Point One-Sided Continuity Test Continuity on an Interval Continuity on a Closed Interval Continuity of a Piecewise Function
Key ideas
Analytical Comparison & Distinction Matrix
| Analytical Method | Standard Representation | Parametric / Invariant Framework |
|---|---|---|
| Algebraic Nature | Explicit equations relating spatial coordinates | Parameterized using scalar parameters (λ, μ) or vectors |
| Symmetry Usage | Relies on coordinate expansion | Exploits vector dot/cross products for rapid simplification |
| Computational Efficiency | Direct for intercept evaluation | Superior for angles, orthogonal projections, and distances |
| Common Mistake | Sign confusion in determinants | Omitting boundary condition checks |
All 41 topics in Continuity & Differentiability
Continuity
- Interval Continuity
- Definition of Continuity of a Function
- Directional Continuity
- Piecewise Functions
Types of Discontinuity
- Non-Removable Discontinuity
- Removable Discontinuity
Continuity of Special Types of Functions
- Continuity of Composite Functions
- Continuity of Functions Involving Exponential Sequence Limits
- Continuity of Functions Involving the Greatest Integer Function
- Continuity of Functions Involving the Signum Function
- Continuity of Functions Defined Differently for Rational & Irrational Inputs
- Properties of Functions Continuous in [a, b]
Intermediate Value Theorem
- Intermediate Value Theorem
Continuity of Addition/Subtraction/Multiplication of Functions
- Continuity of Addition/Subtraction/Multiplication of Functions
Discrete Point Continuity
- Discrete Point Continuity
Extreme Value Theorem
- Extreme Value Theorem
Differentiability
- Relation to Continuity
- First Definition of Derivatives
- Graphical Method
- By Differentiation
- Existence of Derivative
- Point Differentiability
- Piecewise Functions
- Modulus Functions
- Min/Max Functions
- Special Functions
- Non-Differentiable Points
Differentiability in Interval
- Extrema & Differentiability
Differentiability of Addition/Subtraction/Multiplication of Functions
- Product Functions
Functional Equation by Differentiability
- Functional Equation by Differentiability
Theorems of Differentiability
- Theorems of Differentiability
Finding Continuity from Differentiability
- Piecewise Parameter Determination
- Absolute-Value Functions
- Min/Max Functions
- Oscillatory Functions
- Higher-Order Differentiability
- Series Expansion & Cancellation
Finding Non-Differentiability from Discontinuity
- Finding Non-Differentiability from Discontinuity
Standard Results of Differentiability
- Methods of Differentiation
- Implicit Differentiation
- Higher-Order Derivatives