Some of the
main topics for Mathematics chapter Continuity and Differentiability (Class
12) along with their details are:
1. Introduction to
Continuity:
(i)
Concept and Definition of Continuity, (ii) Types of Discontinuities, (iii)
Properties of Continuity
2. Differentiability:
(i)
Concept and Definition of Differentiability, (ii) Properties of
Differentiability, (iii) Relationship between Continuity and Differentiability
3. Chain Rule:
(i)
Derivatives of Composite Functions, (ii) Chain Rule and its Applications
4. Rolle's
Theorem:
(i)
Statement and Proof of Rolle's Theorem, (ii) Applications of Rolle's Theorem
5. Mean Value
Theorem:
(i)
Statement and Proof of Mean Value Theorem, (ii) Lagrange's Mean Value Theorem,
(iii) Applications of Mean Value Theorem
6. Increasing and
Decreasing Functions:
(i)
Definition of Increasing and Decreasing Functions, (ii) First Derivative Test,
(iii) Second Derivative Test
7. Maxima and
Minima:
(i)
Definition of Maxima and Minima, (ii) Finding Local and Absolute Extrema using
Derivatives
8. Derivatives of
Exponential and Logarithmic Functions:
(i)
Derivatives of Exponential and Logarithmic Functions, (ii) Derivatives of
Inverse Trigonometric Functions
9. Rate of
Change:
(i) Rate
of Change and Derivatives, (ii) Related Rates
10. Summary of
Topics:
(i)
Recapitulation of Concepts, (ii) Important Formulas
Overall, this chapter
covers the fundamental concepts of calculus, including the definition and
properties of continuity and differentiability, rules and theorems for taking
derivatives of functions, and finding extrema of functions. It also covers
various applications of differentiation in real-life problems.
More Chapters:-
Main topics for Applications of Derivatives
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other chapters.
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