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Continuity and Differentiability — Study Plan

Madhya Pradesh Board · Class 12 · Mathematics

A step-by-step study plan for Continuity and Differentiability, Madhya Pradesh Board Class 12 Mathematics: what to learn first, what to practise and when.

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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Study Plan

1
Day 1–2

Learn the Theory

Read the textbook chapter carefully. Note down definitions, formulas and key ideas. Focus on: 1. Continuity at a Point and on an Interval, 2. Standard Continuous Functions and Algebra of Continuity, 3. Differentiability and Its Relation to Continuity.

2
Day 3

Practise

Solve the textbook exercises and extra practice questions. There are 114 questions available for this chapter.

3
Day 4

Revise & Test

Revise key points without looking at your notes. Take a practice quiz and mark weak areas for another pass.

4
Day 7

Spaced Revision

Come back to Continuity and Differentiability after a week. Use flashcards for quick recall and try past exam questions on this chapter.

What to Focus On

  • Continuity at c means lim x→c f(x) = f(c).
  • A function is continuous if it is continuous at every point of its domain.
  • At endpoints of [a, b], one-sided limits are used.
  • Discontinuity can come from jump, hole, or mismatch of values and limits.
  • +∞ and −∞ are not real numbers.
  • A function defined everywhere is not automatically continuous.
  • Derivative at c is defined by a limit of the difference quotient.
  • Differentiability implies continuity.
  • Continuity does not imply differentiability.

Common Mistakes to Avoid

If a function is defined at a point, it is continuous at that point.

A continuous function is always differentiable.

To prove continuity, it is enough to substitute x = c into the formula.

Memory Tips

Continuity at a point

Discontinuity terminology

Continuity on a closed interval

Every differentiable function is continuous

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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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