Left-hand and right-hand limits (Ex 12.1 Q23)बाएँ और दाएँ पक्ष की सीमाएँ (प्रश्नावली 12.1 प्रश्न 23)Left-hand and right-hand limits (Ex 12.1 Q23)

Section 12.3 · Class 11 Maths Ch 12 · interactive diagram

Parts and what they mean

• Left piece (बायाँ भाग) — For x ≤ 0, f(x) = 2x + 3. Approaching 0 from the left: LHL = 3.
• Right piece (दायाँ भाग) — For x > 0, f(x) = 3(x + 1). Approaching 0 from the right: RHL = 3.
• Both sides meet (दोनों पक्ष मिलते हैं) — LHL = RHL = 3, so lim (x→0) f(x) = 3.
• Existence of a limit (सीमा का अस्तित्व) — lim (x→a) f(x) exists exactly when the left and right limits are equal. In Q24–26 they differ, so the limit does not exist.

Original diagram drawn by Simple Learning Hub for NCERT Class 11 Maths Ch 12. Report a mistake