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1.Concept of Limits
Class 11 • Mathematics • NCERT
Concept of Limits
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This lesson introduces the concept of limits as per NCERT Class 11. Students learn the intuitive meaning of limits, left-hand and right-hand limits, and evaluate simple limits using algebraic methods.
Lesson Objectives
- Understand the intuitive idea of limits.
- Learn left-hand and right-hand limits.
- Evaluate simple limits algebraically.
- Build a foundation for derivatives.
1. What Is a Limit?
The limit of a function describes the value that the function approaches as the input approaches a certain value.
We write:
limx→a f(x) = L
limx→a f(x) = L
2. Intuitive Meaning of Limits
The value of a function at x = a may or may not exist, but the limit depends only on the values of the function near x = a.
Limit focuses on approaching, not necessarily reaching.
3. Left-Hand and Right-Hand Limits
If a function approaches the same value from both sides, the limit exists.
Left-hand limit: limx→a⁻ f(x)
Right-hand limit: limx→a⁺ f(x)
Right-hand limit: limx→a⁺ f(x)
4. When Does a Limit Exist?
A limit exists at x = a if:
• Left-hand limit exists
• Right-hand limit exists
• Both are equal
• Right-hand limit exists
• Both are equal
5. Simple NCERT Examples
• limx→2 (x + 3) = 5
• limx→1 (x² − 1)/(x − 1) = 2
Practice Questions (NCERT)
- What is a limit?
- Does limit depend on the value of function at the point?
- Define left-hand limit.
- Define right-hand limit.
- When does a limit exist?
- Evaluate limx→3 (2x + 1).
- Evaluate limx→1 (x² + x).
- Can a limit exist if LHL ≠ RHL?
- What is limx→0 x?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- The value approached by a function.
- No
- Limit as x approaches from left.
- Limit as x approaches from right.
- When LHL = RHL.
- 7
- 2
- No
- 0
- Yes
© Aviate Learning – Limits & Derivatives (NCERT Class 11)