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Continuity and Differentiability — Revision Notes

Madhya Pradesh Board · Class 12 · Mathematics

Continuity and Differentiability revision notes for Madhya Pradesh Board Class 12 Mathematics: 4 topics in quick points.

114 questions54 flashcards17 formulas & key relations5 concepts

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A step-by-step flowchart for applying logarithmic differentiation to functions of the form y = u(x)^v(x) or complex products/quotients.
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Key Topics to Revise

1

1. Continuity at a Point and on an Interval

  • A function is continuous at a point when its limit at that point equals its value there.
  • A function is continuous if it is continuous at every point of its domain.
  • For a closed interval [a,b], continuity at the endpoints is checked using one-sided limits.
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2. Standard Continuous Functions and Algebra of Continuity

  • Every polynomial function is continuous.
  • Every rational function is continuous wherever its denominator is nonzero.
  • The sine function is continuous everywhere.
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3. Differentiability and Its Relation to Continuity

  • The derivative at a point is defined as a limit of the difference quotient, if the limit exists.
  • A function is differentiable at a point when this limit exists.
  • A function is differentiable in an interval if it is differentiable at every point of the interval.
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4. Chain Rule and Derivatives of Composite Functions

  • The chain rule is the main tool for differentiating composite functions.
  • If f = v∘u and t = u(x), then df/dx = (dv/dt)(dt/dx).
  • For three composed functions, multiply the derivatives step by step.

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Full Notes

Key Concepts

A function is continuous atA function is continuous if itIf a function is not continuousSumThe derivative at c is defined

Frequently Asked Questions

What are the important topics in Continuity and Differentiability for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Continuity and Differentiability include Continuity at a Point and on an Interval, Standard Continuous Functions and Algebra of Continuity, Differentiability and Its Relation to Continuity, Chain Rule and Derivatives of Composite Functions. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How should I revise Continuity and Differentiability for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 114 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 Madhya Pradesh Board Class 12 Mathematics Revision Notes

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