y = 1/x near 0: shoots to +∞ and −∞0 के पास y = 1/x: +∞ और −∞ की ओर0 ke paas y = 1/x: +∞ aur −∞ ki taraf

NCERT Fig 5.3 · 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.
• Branch for x > 0 (x > 0 वाली शाखा) — Values 1, 3.333\ldots, 5, 10, 100, \ldots as x goes 1, 0.3, 0.2, 0.1, 0.01, \ldots
• Branch for x < 0 (x < 0 वाली शाखा) — Values -1, -3.333\ldots, -5, -10, \ldots as x comes to 0 from the left.
• \lim_{x \to 0^+} \frac{1}{x} = +\infty (\lim_{x \to 0^+} \frac{1}{x} = +\infty) — +\infty is NOT a real number, so this right hand limit does not exist.
• \lim_{x \to 0^-} \frac{1}{x} = -\infty (\lim_{x \to 0^-} \frac{1}{x} = -\infty) — -\infty is NOT a real number either; 0 is not in the domain of \frac{1}{x}.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 5.3. Report a mistake