JEE Limits Quiz
Practice on evaluating limits, standard results, indeterminate forms, L'Hopital's rule, and the link between limits, continuity and differentiability.
Skill map
Levels in this jee limits quiz
Every question is generated fresh by AI and calibrated to your level - clear a level and the next one gets harder. Miss one and the AI tutor explains Limits until it sticks, then aims a follow-up at the gap. Want to grind one level? Start the quiz and type that sub-topic as your own.
Exam focus
How Limits is asked
The entry point to Calculus, which is the largest single block in JEE Mathematics. Questions frequently combine limits with continuity and differentiability at a point, so preparing them as one topic rather than three matches how they are asked.
Cheat sheet
Limits formulas worth memorising
| Quantity | Formula |
|---|---|
| Standard limit | lim(x→0) sin x / x = 1 |
| Standard limit | lim(x→0) (1 − cos x)/x² = ½ |
| Standard limit | lim(x→0) (eˣ − 1)/x = 1 |
| Standard limit | lim(x→0) ln(1 + x)/x = 1 |
| Exponential limit | lim(x→∞) (1 + 1/x)ˣ = e |
| L'Hopital's rule | for 0/0 or ∞/∞, lim f/g = lim f′/g′ |
| Continuity at a | LHL = RHL = f(a) |
Marks lost here
Common mistakes in Limits
- Applying L'Hopital's rule to a form that is not indeterminate. It is valid only for 0/0 and ∞/∞; using it on 2/3 produces nonsense, and forms like 1^∞ must be converted through logarithms first.
- Using sin x / x → 1 when x is in degrees. The standard limit holds in radians only, which is why calculus is done in radians throughout.
- Assuming a function continuous at a point is differentiable there. |x| is continuous everywhere and not differentiable at zero; differentiability implies continuity but never the reverse.
- Ignoring one-sided limits at a piecewise boundary. The limit exists only if the left- and right-hand limits agree, and piecewise functions are set precisely to test that.
- Cancelling a factor without noting the domain restriction. (x² − 1)/(x − 1) simplifies to x + 1 for the limit, but the original function is still undefined at x = 1.
Game rules
How a round works
- 01Spawn
Press play - the AI generates Limits questions in seconds.
- 02Level up
Answer to earn XP and build a streak. Difficulty adapts to your accuracy and speed.
- 03Learn or lose
Every answer - right or wrong - gets an AI tutor explanation. Wrong answers respawn as follow-ups.
Leaderboard
Limits high scores
Next challenges
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Player's guide
JEE Limits Quiz - FAQs
When is L'Hopital's rule the wrong tool?
When the limit is not indeterminate, and often when a standard limit or a series expansion would be faster. Repeatedly differentiating a messy quotient can be slower than substituting sin x ≈ x − x³/6 and reading off the leading behaviour.
What is the relationship between continuity and differentiability?
Differentiability at a point implies continuity there, but not the other way round. A function can be continuous yet have a corner, as |x| does at the origin, where the left and right derivatives differ.
Is the jee limits quiz free?
Yes - completely free, with no sign-up required. Type a topic, press start, and the AI generates an adaptive Limits quiz with an explanation for every answer.
Can teachers host this jee limits quiz live for a class?
Yes - create a free teacher account, host a live room on "Limits", and students join with a 6-character code at quff.in/join. No student accounts needed.
From the blog
Limits guides & reading
JEE Limits: 30 Practice Questions with Full Solutions
Thirty solved Limits questions, starting from the check that decides the method: is the form actually indeterminate?
Exam PrepJEE Differentiation: 30 Practice Questions with Solutions
Thirty solved Differentiation questions, weighted toward applications of derivatives - which is where the paper actually puts its marks.
Exam PrepJEE Integration: 30 Practice Questions with Solutions
Thirty solved Integration questions, organised around the only decision that matters: which technique the integrand is asking for.
More exam prep quizzes
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