Do both sides agree?
"Do both sides agree?" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Left and right hand limits" in Limits and Derivatives. Pick a function and move x towards the point a, first from the left (d negative), then from the right. Watch the height the orange dot heads for on each side, and compare it with the filled dot, the actual value f(a). The limit at a exists only when the left and right hand limits exist and are equal. It never depends on f(a), which may differ from the limit or not exist at all. JEE Main asked 24 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Left and right hand limits in Limits and Derivatives. Change the values and watch what happens.
In JEE Main
42 shifts analysed
24 questions from Limits and Derivatives across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §12.3
- Approaching a from values less than a gives the left hand limit, written lim_{x→a⁻} f(x). Approaching from values greater than a gives the right hand limit, lim_{x→a⁺} f(x).
- lim_{x→a} f(x) exists only when both one-sided limits exist and are equal; that common number is the limit.
- For f(x) = 1 when x ≤ 0 and f(x) = 2 when x > 0, the left hand limit at 0 is 1 and the right hand limit is 2, so the limit at 0 does not exist.
- Worked: f(x) = x − 2 for x < 0, 0 at x = 0, and x + 2 for x > 0. At 0 the left hand limit is −2 and the right hand limit is 2, so there is no limit, although f(0) = 0.
- Worked: f(x) = x + 2 for x ≠ 1 and f(1) = 0. Both one-sided limits at 1 are 3, so the limit is 3, which differs from f(1). A limit and a value can disagree.
Questions
3 answers
- What does the "Do both sides agree?" simulation show?
- Pick a function and move x towards the point a, first from the left (d negative), then from the right. Watch the height the orange dot heads for on each side, and compare it with the filled dot, the actual value f(a).
- Does JEE Main ask questions from Limits and Derivatives?
- Yes. JEE Main asked 24 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Left and right hand limits" in Limits and Derivatives (Class 11 Maths).
Embed this simulation
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Teaching this idea? Put the simulation on your own page or LMS with this code.