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Revision Notes

Limits

Maharashtra Board · Class 11 · Mathematics & Statistics

Quick revision notes for Limits — Maharashtra Board Class 11 Mathematics & Statistics. Key concepts, formulas, and definitions for last-minute revision.

45 questions20 flashcards5 concepts

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Key Topics to Revise

1

Definition and Basic Concepts of Limits

  • A limit describes the value a function approaches as the input approaches a specific value
  • The notation lim(x→a) f(x) = L means f(x) approaches L as x approaches a
  • x → a means x takes values very close to 'a' but never equals 'a'
2

Algebra of Limits

  • Limit of sum equals sum of limits: lim[f(x) + g(x)] = lim f(x) + lim g(x)
  • Limit of product equals product of limits: lim[f(x) × g(x)] = lim f(x) × lim g(x)
  • Limit of quotient equals quotient of limits (when denominator limit ≠ 0)
3

Direct Substitution Method

  • Simplest method: substitute x = a directly in f(x)
  • Works when f(x) is continuous at x = a
  • Applicable for polynomial functions, rational functions where denominator ≠ 0
4

Factorization Method

  • Used when direct substitution gives 0/0 form
  • Factor both numerator and denominator to find common factors
  • Cancel common factors (since x ≠ a, the factor (x-a) ≠ 0)

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Full Notes

Key Concepts

If f(x) approaches a finite valueLeftIf lim(x→a) f(x) = lWhen Q(a) ≠ 0 for rationalUsed when direct substitution gives 0/0

Frequently Asked Questions

What are the important topics in Limits for Maharashtra Board Class 11 Mathematics & Statistics?
Limits 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.
How to score full marks in Limits — Maharashtra Board Class 11 Mathematics & Statistics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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