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Limits — Revision Notes

ICSE · Class 11 · Mathematics

Limits revision notes for ICSE Class 11 Mathematics: 4 topics in quick points. Part of the ICSE Class 11 Mathematics syllabus.

60 questions31 flashcards15 formulas & key relations5 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.
2

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.
3

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.
4

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 Core Idea of Limit, Algebra of Limits, Methods for Evaluating Algebraic Limits, Standard Trigonometric Limits and Their Use. Study these first, then practise questions on each for Class 11 exams.
How should I revise Limits for Class 11 exams?
Learn the core ideas first, then work through the 60 practice questions on Limits. Revise 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 ICSE Class 11 Mathematics Revision Notes

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