Limits And Continuity
Kerala Board · Class 12 · Mathematics
Quick revision notes for Limits And Continuity — Kerala Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Fundamental Concepts of Limits
- A limit describes the value a function approaches as the input approaches a specific value
- Limits can exist even when the function is not defined at that point
- The notation lim(x→a) f(x) = L means f(x) approaches L as x approaches a
Methods for Evaluating Limits
- Direct Substitution: Works when function is defined at the point
- Factorization Method: Used for 0/0 forms by canceling common factors
- Rationalization Method: Used when square roots are present
Continuity of Functions
- A function is continuous at x = a if lim(x→a) f(x) = f(a)
- Three conditions for continuity: f(a) exists, limit exists, limit equals f(a)
- Discontinuity types: Removable, Jump, Infinite
Problem-Solving Strategies and Techniques
- Systematic approach: Identify form, choose method, apply technique, verify result
- For 0/0 forms: Factor, rationalize, or use standard limits
- For ∞/∞ forms: Divide by highest power or use L'Hôpital's rule
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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