JEE Main Limits and Continuity 2027 — Standard Limits, Differentiability and Practice Questions

April 12, 2026 · CUET Gurukul · JEE-2027 Blog

JEE Gurukul — Maths Chapter Guide

JEE Main 2027 Exam Relevance: Limits and Continuity is a fundamental chapter in Calculus — 3-4 questions in JEE Main. These questions are often easy to medium difficulty and highly scoring.

JEE Main Limits and Continuity 2027 — Key Concepts and Formulas

Limits and Continuity forms the foundation of Calculus in JEE Mathematics. Master the standard limits, L’Hôpital’s Rule, and continuity conditions to score well in this predictable chapter.

Standard Limits — Must Memorize

Limit	Value
lim(x→0) (sin x)/x	1
lim(x→0) (tan x)/x	1
lim(x→0) (e^x – 1)/x	1
lim(x→0) (a^x – 1)/x	ln a
lim(x→∞) (1 + 1/x)^x	e
lim(x→0) (ln(1+x))/x	1

Continuity — Three Conditions

A function f(x) is continuous at x = a if and only if:

f(a) is defined (exists)
lim(x→a) f(x) exists (LHL = RHL)
lim(x→a) f(x) = f(a)

JEE Gurukul Tip: Discontinuity types are frequently tested: Removable (limit exists, f(a) ≠ limit), Jump (LHL ≠ RHL), Infinite (limit → ∞). Non-differentiable but continuous: |x| at x=0, x^(1/3) at x=0. The derivative at a point requires continuity — but continuity alone doesn’t guarantee differentiability.

L’Hôpital’s Rule — When to Apply

Apply L’Hôpital’s Rule only for 0/0 or ∞/∞ indeterminate forms: differentiate numerator and denominator separately (not as a quotient), then take the limit again. Common mistakes: applying it for non-indeterminate forms, or forgetting to re-check if another application is needed.

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