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Revision Notes

Limits

ICSE · Class 11 · Mathematics

Quick revision notes for Limits — ICSE Class 11 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

60 questions31 flashcards5 concepts

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A graph of a function f(x) with a removable discontinuity (a hole) at x=a. Show arrows on the x-axis indicating x approaching 'a' from both the left and the right. Corresponding arrows on the y-axis s
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Key Topics to Revise

1

1. Core Idea of Limit

  • A limit describes the value a function approaches as x approaches a number c.
  • Limit is written as lim_{x->c} f(x).
  • A real number can be approached very closely without being exactly equal to it.
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2. Algebra of Limits

  • Limits follow sum, difference, product, and quotient rules.
  • These rules apply when the individual limits exist.
  • For the quotient rule, the denominator limit must not be zero.
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3. Methods for Evaluating Algebraic Limits

  • Direct substitution works when the function is defined at the point.
  • Factorisation is used mainly when substitution gives 0/0 form.
  • Rationalisation is used when square roots are involved.
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4. Standard Trigonometric Limits and Their Use

  • The key trigonometric limit is lim_{x->0}(sin x/x) = 1.
  • Another standard limit is lim_{x->0}((1-cos x)/x) = 0.
  • Also, lim_{x->0}(tan x/x) = 1.

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Full Notes

Key Concepts

The limit of a function fIf limits of two functions existIf a lies in the domainWhen direct substitution gives 0/0For expressions containing square roots

Frequently Asked Questions

What are the important topics in Limits for ICSE Class 11 Mathematics?
Key topics in Limits include Mind map showing diverse real-world applications of limit concepts across different fields, Limits Classification and Methods, Limits: Methods and Applications Overview. These are the concepts ICSE Class 11 examiners draw on most — study them first, then practise related questions.
How to score full marks in Limits — ICSE Class 11 Mathematics?
Understand the core concepts first, then work through the 60 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall 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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All 18 chapters — ICSE Class 11 Mathematics Revision Notes

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