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Continuity and Differentiability

Madhya Pradesh Board · Class 12 · Mathematics

Quick revision notes for Continuity and Differentiability — Madhya Pradesh Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

114 questions54 flashcards5 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.
3

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?
Continuity and Differentiability covers several key topics that are frequently asked in Madhya Pradesh Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Continuity and Differentiability — Madhya Pradesh Board Class 12 Mathematics?
Understand the core concepts first, then work through the 114 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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