Continuity and Differentiability
Karnataka Board · Class 12 · Mathematics
Quick revision notes for Continuity and Differentiability — Karnataka Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Continuity of Functions
- A function f(x) is continuous at point c if lim(x→c) f(x) = f(c)
- For continuity at c: left-hand limit = right-hand limit = function value at c
- Graphically, continuous functions can be drawn without lifting the pen
Differentiability
- A function is differentiable at c if lim(h→0) [f(c+h) - f(c)]/h exists
- Every differentiable function is continuous, but not vice versa
- Differentiability implies continuity but continuity doesn't guarantee differentiability
Chain Rule
- Used to differentiate composite functions f(g(x))
- If y = f(u) and u = g(x), then dy/dx = (dy/du) × (du/dx)
- Essential for differentiating complex functions
Derivatives of Inverse Trigonometric Functions
- Inverse trigonometric functions have specific derivative formulas
- Domain restrictions are important for these functions
- Often combined with chain rule for composite functions
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Continuity and Differentiability covers several key topics that are frequently asked in Karnataka Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- 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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