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Limits And Continuity — Study Plan

Telangana Open School (TOSS) · Class 12 · Mathematics

A step-by-step study plan for Limits And Continuity, Telangana Open School (TOSS) Class 12 Mathematics: what to learn first, what to practise and when.

53 questions25 flashcards12 formulas & key relations4 concepts

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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: Understanding Limits, Continuity of Functions.

2
Day 3

Practise

Solve the textbook exercises and extra practice questions. There are 53 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 Limits And Continuity after a week. Use flashcards for quick recall and try past exam questions on this chapter.

What to Focus On

  • Limit is about the behavior of a function near a point, not at the point.
  • The limit exists only if left-hand and right-hand limits are equal.
  • A function may not be defined at a point, but its limit may still exist there.
  • Left-hand limit: x approaches a from the left (x < a).
  • Right-hand limit: x approaches a from the right (x > a).
  • Limit exists ⇔ LHL = RHL.
  • Direct substitution works when the function is continuous at the point.
  • Factorisation removes common factors causing 0/0 form.
  • Rationalisation helps eliminate square roots in indeterminate forms.

Common Mistakes to Avoid

If a function is undefined at a point, the limit at that point cannot exist.

Left-hand limit and right-hand limit are the same if the function looks continuous on a graph.

You can always substitute x = a directly to find limₓ→ₐ f(x).

Memory Tips

Definition of a Limit

Left-Hand Limit (LHL)

Right-Hand Limit (RHL)

Existence of Limit

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Frequently Asked Questions

What are the important topics in Limits And Continuity for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Limits And Continuity include Understanding Limits, Continuity of Functions. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Limits And Continuity for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 53 practice questions on Limits And Continuity. 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.

More resources for Limits And Continuity

All Telangana Open School (TOSS) Class 12 Mathematics Study Plan

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