Limits for JEE

• Check the form first: 0/0, ∞/∞, 1^∞
• 1^∞ form: limit = e^(lim (f − 1)g)
• Use standard limits before L'Hôpital
• Expansions (series) solve many limits quickly

• lim sin x / x = 1, lim (1 − cos x)/x² = ½
• lim (eˣ − 1)/x = 1, lim ln(1 + x)/x = 1
• lim (1 + x)^(1/x) = e
• lim (aˣ − 1)/x = ln a

Printable Limits formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

• Using L'Hôpital when the form is not indeterminate
• Forgetting degrees vs radians
• Sign errors with left and right limits

Appears frequently. Series expansions of sin x, cos x, eˣ and ln(1 + x) to the x³ term save a lot of time.

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Question. Evaluate lim(x→0) [(e^(sin x) - e^(tan x)) / x³]

This example was solved twice independently and both solutions agree.

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

• LIMIT, CONTINUITY & DIFFERENTIABILITY in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 6:35:05
  Jump to a subtopic (25)

  • 00:00 Introduction
  • 04:57 Topics to be covered
  • 07:19 Limit at a point x=a
  • 36:24 Some standard limits
  • 1:23:21 Exponential limits
  • 1:34:54 Logarithmic limits
  • 1:46:48 Algebraic limits
  • 1:52:56 Various methods to solve limits
  • 2:10:52 Solving limits using L’Hospital rule
  • 2:11:23 Indeterminate forms
  • 2:46:15 Solving limits of the form 1 power infinity
  • 3:00:50 Solving limits using series expansion
  • 3:23:26 Solving limits using sandwich theorem
  • 3:32:45 Continuity at a point x=a
  • 3:53:59 Continuity in an interval
  • 4:19:24 Properties of continuous function
  • 4:32:45 Break
  • 5:02:27 Differentiability at a point x=a and In an interval
  • 5:19:38 Geometrical interpretation of differentiability
  • 5:20:48 Continuity Vs Differentiatiability
  • 5:44:52 Continuity over an interval
  • 5:55:14 Properties of differentiable function
  • 6:08:38 Functional identities
  • 6:33:00 Homework
  • 6:33:43 Thank You Bacchon
• Limits Class 11 | One Shot | JEE Main & Advanced | Arvind Kalia Sir — JEE Nexus by Unacademy, 2:42:50

• 5 JEE Main 2026 PYQs on Limits, with solutions.
• Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
• Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
• Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
• See it move: interactive simulation.