Example 10: jump at x = 1उदाहरण 10: x = 1 पर छलाँगExample 10: x = 1 par jump

NCERT Fig 5.4 · 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) = x + 2 for x \le 1 (x \le 1 के लिए f(x) = x + 2) — A polynomial piece — continuous at every c < 1.
• f(x) = x - 2 for x > 1 (x > 1 के लिए f(x) = x - 2) — Continuous at every c > 1.
• LHL = f(1) = 3 (LHL = f(1) = 3) — \lim_{x \to 1^-} (x + 2) = 3, the filled dot.
• RHL = -1 (RHL = -1) — \lim_{x \to 1^+} (x - 2) = -1; open dot, not a value of f.
• Jump of 4 at x = 1 (x = 1 पर 4 की छलाँग) — 3 \ne -1: x = 1 is the only point of discontinuity.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 5.4. Report a mistake