Chapter 9 of 42
Syllabus
Limits — Syllabus
JEE Mains · Mathematics
Free Limits syllabus for JEE Mains Mathematics 2026 — topics covered, weightage, and preparation priorities for this chapter.
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Get startedLimits — Syllabus & Topics
Topics covered in Limits for JEE Mains Mathematics.
Topics in Limits
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1. Neighbourhood and Basic Concept of Limits
- Neighbourhood of a real number 'a' is the interval (a-δ, a+δ) where δ > 0
- Left neighbourhood: (a-δ, a) and Right neighbourhood: (a, a+δ)
- x → a⁻ means x approaches 'a' from the left side
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2. Algebra of Limits and Direct Substitution
- If limits exist, they follow algebraic operations: sum, difference, product, quotient
- Direct substitution works when function is continuous at the point
- Use algebraic properties only when individual limits exist
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3. Sandwich Theorem (Squeeze Theorem)
- If f(x) ≤ g(x) ≤ h(x) and lim f(x) = lim h(x) = L, then lim g(x) = L
- Particularly useful for functions involving sine, cosine with other expressions
- Functions need not satisfy inequality at the point, only in neighborhood
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4. Indeterminate Forms and Their Evaluation
- Indeterminate forms: 0/0, ∞/∞, 0×∞, ∞-∞, 0⁰, 1^∞, ∞⁰
- Factorization method: Cancel common factors causing indeterminate form
- Rationalization: Multiply by conjugate for expressions with square roots
Key Concepts
A neighborhood Nδ(a) = (aA limit exists at x =When f(x) is continuous at xIf f(x) ≤ g(x) ≤ h(x)Forms like 0/0
Frequently Asked Questions
What topics are covered in Limits for JEE Mains?
Limits is an important chapter in JEE Mains Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: 1. Neighbourhood and Basic Concept of Limits, 2. Algebra of Limits and Direct Substitution, 3. Sandwich Theorem (Squeeze Theorem), 4. Indeterminate Forms and Their Evaluation.
How important is Limits for JEE Mains?
Limits is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 68 practice questions available for this chapter.
How to prepare Limits for JEE Mains?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.
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