6th Maths NCERT Chapter 5

Topics to Study in Chapter 5: Continuity and Differentiability

1. Introduction to Differentiability, Continuity, and Inverse Trigonometric Functions

– Summary: This chapter builds on differentiation concepts from Class XI, covering continuity, differentiability, and relations between them. It includes differentiation of inverse trigonometric functions and introduces exponential and logarithmic functions.

2. Continuity

– Summary: Defines continuity at a point mathematically using left and right-hand limits and the function's value at that point. Discusses points of discontinuity and provides examples to illustrate continuity testing methods.

3. Examples of Testing Continuity

– Summary: Provides examples demonstrating how to check the continuity of functions at specific points, including calculations of limits and comparisons with function values.

4. Continuity of Constant and Identity Functions

– Summary: Examines the continuity of constant functions and the identity function, showing that constant functions are continuous everywhere, while the identity function is continuous at all real numbers.

5. Continuity of Functions on Closed Intervals

– Summary: Expands the definition of continuity to functions defined on closed intervals [a, b], clarifying the conditions for continuity at the endpoints of the interval.

6. Continuity of a Real Function

– Summary: Defines a real function as continuous if it is continuous at every point in its domain, providing a comprehensive understanding of continuity for functions.

These topics cover the essential concepts and examples related to continuity and differentiability discussed in the chapter. Students can focus on understanding the definitions, testing continuity, and identifying points of discontinuity to have a solid grasp of the material.