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Continuity and Differentiability — Revision Notes

ICSE · Class 12 · Mathematics

Continuity and Differentiability revision notes for ICSE Class 12 Mathematics: 4 topics in quick points. Part of the ICSE Class 12 Mathematics syllabus.

105 questions29 flashcards9 formulas & key relations5 concepts

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A graph of a continuous function at a specific point, showing the limit approaching the function value, illustrating that the function is unbroken and defined at that point.
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Key Topics to Revise

1

1. Limits and One-Sided Limits

  • A limit describes the real number that a function approaches as x approaches a point c.
  • A limit exists only when both the left-hand limit and the right-hand limit exist and are equal.
  • Right-hand limit means approaching c from the right side.
2

2. Continuity at a Point and on an Interval

  • A function is continuous at x=c when the limit at c equals the function value at c.
  • For continuity, both the limit and f(c) must exist and be equal.
  • A function is right continuous if the right-hand limit equals the function value.
3

3. Algebra of Continuous Functions

  • Sum, difference, and product of continuous functions are continuous.
  • A quotient of continuous functions is continuous if the denominator is non-zero.
  • 1/f is continuous if f(c)≠0.
4

4. Differentiability at a Point and One-Sided Derivatives

  • Differentiability at x=c means the derivative limit exists finitely.
  • The derivative exists only when both one-sided derivatives exist finitely and are equal.
  • Right differentiable and left differentiable are one-sided versions of differentiability.

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Full Notes

Key Concepts

A function approaches a real numberThe rightA function is continuous at xA function is discontinuous if f(c)A removable discontinuity occurs when

Frequently Asked Questions

What are the important topics in Continuity and Differentiability for ICSE Class 12 Mathematics?
Key topics in Continuity and Differentiability include Limits and One-Sided Limits, Continuity at a Point and on an Interval, Algebra of Continuous Functions, Differentiability at a Point and One-Sided Derivatives. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How should I revise Continuity and Differentiability for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 105 practice questions on Continuity and Differentiability. 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 12 Mathematics Revision Notes

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