Simulation · Maths · Class 11

Do both sides agree?

From the lesson Left and right hand limits in Limits and Derivatives. Change the values and watch what happens.

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.

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