Continuity
Maharashtra Board · Class 11 · Mathematics & Statistics
Quick revision notes for Continuity — Maharashtra Board Class 11 Mathematics & Statistics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Definition and Conditions for Continuity
- A function f(x) is continuous at x = a if three conditions are satisfied simultaneously
- Continuity means the graph has no breaks, holes, or jumps at that point
- Left-hand limit must equal right-hand limit and both must equal the function value
Types of Discontinuities
- Jump discontinuity occurs when left and right limits exist but are different
- Removable discontinuity can be 'fixed' by redefining the function at one point
- Infinite discontinuity occurs when function approaches ±∞
Continuity Problem-Solving Techniques
- Systematic approach: check definition, calculate limits, compare values
- For piecewise functions, focus on boundary points where definition changes
- Use algebraic manipulation to resolve indeterminate forms
Continuity Over Intervals
- Continuity on open interval (a,b) means continuous at every point inside
- Continuity on closed interval [a,b] requires right-continuity at a and left-continuity at b
- Half-open intervals need appropriate one-sided continuity at endpoints
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Continuity covers several key topics that are frequently asked in Maharashtra Board Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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