Limits agree, but f(0) is somewhere elseसीमाएँ बराबर, पर f(0) कहीं औरLimits barabar, par f(0) kahin aur

NCERT Fig 5.2 · Class 12 Maths · Chapter 5 · interactive diagram

Parts and what they mean

• x-axis (x-अक्ष) — The horizontal number line; inputs x are read here.
• y-axis (y-अक्ष) — The vertical number line; outputs y = f(x) are read here.
• Origin O(0, 0) (मूल बिंदु O(0, 0)) — Where the two axes cross.
• f(x) = 1 for x \ne 0 (x \ne 0 के लिए f(x) = 1) — Everywhere except 0 the value is 1.
• Hole: LHL = RHL = 1 (छिद्र: LHL = RHL = 1) — From both sides the graph heads to 1, so \lim_{x \to 0} f(x) = 1.
• Value f(0) = 2 (मान f(0) = 2) — The limit 1 does not equal the value 2, so f is not continuous at 0.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 5.2. Report a mistake