Last Updated: April 2026
Limits and Continuity (Chapter 13, Class 11 NCERT) along with Differentiation forms the Calculus backbone of JEE Main Mathematics. In JEE Main 2025, Calculus contributed 8–10 questions — 32–40 marks — making it the single highest-weight area in JEE Maths. A solid foundation in Limits is essential before tackling Derivatives and Integration.
JEE Main Mathematics Chapter-wise Weightage
| Area | Chapters | Avg Questions | Marks |
|---|---|---|---|
| Calculus | Limits, Derivatives, Integration, Differential Equations | 8–10 | 32–40 |
| Algebra | Complex Numbers, Matrices, Sequences, Permutations | 7–8 | 28–32 |
| Coordinate Geometry | Straight Lines, Circles, Conics | 5–6 | 20–24 |
| Trigonometry | Trig functions, Equations, Properties of Triangles | 3–4 | 12–16 |
| 3D Geometry and Vectors | Vectors, 3D Lines and Planes | 3–4 | 12–16 |
Limits — Standard Forms and Results
| Limit Form | Result | Condition |
|---|---|---|
| lim(x→0) sinx/x | 1 | x in radians |
| lim(x→0) tanx/x | 1 | x in radians |
| lim(x→0) (1-cosx)/x² | 1/2 | Standard result |
| lim(x→0) (eˣ-1)/x | 1 | Exponential standard form |
| lim(x→0) (aˣ-1)/x | ln a | Generalised form |
| lim(x→0) ln(1+x)/x | 1 | Logarithm standard form |
| lim(x→∞) (1 + 1/x)ˣ | e | Definition of e |
| lim(x→0) (1 + x)^(1/x) | e | Equivalent form |
L’Hopital’s Rule — When and How to Apply
Apply L’Hopital’s Rule when a limit gives 0/0 or ∞/∞ indeterminate form:
- Step 1: Verify the limit gives 0/0 or ∞/∞
- Step 2: Differentiate numerator and denominator separately
- Step 3: Evaluate the new limit
- Step 4: Repeat if still indeterminate
Example: lim(x→0) sinx/x gives 0/0 → apply L’Hopital → lim(x→0) cosx/1 = cos0 = 1
Continuity — Key Conditions
A function f(x) is continuous at x = a if ALL three conditions hold:
- f(a) is defined (function exists at the point)
- lim(x→a) f(x) exists (left limit = right limit)
- lim(x→a) f(x) = f(a) (limit equals function value)
Types of Discontinuity — JEE Classification
| Type | Description | Example |
|---|---|---|
| Removable Discontinuity | Limit exists but ≠ f(a), or f(a) undefined | f(x) = sinx/x at x=0 |
| Jump Discontinuity | Left limit ≠ Right limit (both finite) | Floor function at integers |
| Infinite Discontinuity | Limit is ∞ | f(x) = 1/x at x=0 |
JEE Maths Limits — 5 Practice Problems
- Find lim(x→0) (sin3x)/x → Apply standard form: = 3 × lim(sin3x/3x) = 3 × 1 = 3
- Find lim(x→2) (x²-4)/(x-2) → Factor: (x+2)(x-2)/(x-2) = lim(x→2)(x+2) = 4
- Is f(x) = |x| continuous at x = 0? Yes — LHL = RHL = f(0) = 0. Continuous but not differentiable.
- Find lim(x→∞) (3x²+2x)/(x²+1) → Divide by x²: = (3+2/x)/(1+1/x²) → 3 as x→∞
- Find lim(x→0) (e^(2x)-1)/x → Standard form: 2 × lim(e^(2x)-1)/(2x) = 2×1 = 2
Frequently Asked Questions — JEE Maths Limits
How many Calculus questions come in JEE Main?
Calculus (Limits, Derivatives, Integration, Differential Equations) contributes 8–10 questions in JEE Main Mathematics — approximately 35–40% of total Maths marks. Integration alone typically has 3–4 questions. This makes Calculus the single most important area to master for JEE Main 2026.
What is the best way to prepare Limits for JEE Main?
For JEE Main Limits: (1) Memorise all 8 standard limit forms. (2) Practice substitution, factorisation, and L’Hopital techniques. (3) Solve 50+ problems from standard forms. (4) Practice mixed problems from previous year JEE Main papers. The chapter is highly formulaic — pattern recognition is key.
Is continuity a separate topic from limits in JEE?
Continuity is closely linked to limits — you cannot understand continuity without limits. In JEE, 1–2 questions typically combine both: testing whether a function is continuous at a point requires calculating left and right limits and comparing with the function value. Both topics are covered in NCERT Class 11 Chapter 13.
Master JEE Mathematics with topic-wise practice at JEE Gurukul.
