Functions and Limits Notes for Class 12 & IIT JEE

The limit of f(x) as x approaches a is the value f(x) approaches — it does not require f(a) to be defined. The value of the function is simply f(a). A function can have a limit at a point where it is not defined, and the limit and function value can differ even when both exist.

Functions and Limits typically contribute 2–3 direct questions per JEE Mains attempt, based on NTA papers from 2019 to 2024. These span domain/range, evaluation of limits, and continuity. Because the same concepts appear inside Differentiation and Integration questions, effective preparation here multiplies your returns across multiple questions.

No. L'Hôpital's Rule applies only to 0/0 and ∞/∞ indeterminate forms. JEE Mains also tests 1^∞, 0×∞, ∞−∞, and 0⁰ forms, each requiring a specific conversion before L'Hôpital can be used — or a direct application of standard limit formulas. Over-relying on L'Hôpital without checking the form first is a common error that leads to wrong answers.

A removable discontinuity occurs when the limit of f(x) at x = a exists but either f(a) is undefined, or f(a) ≠ the limit. It is called "removable" because redefining f(a) equal to the limit makes the function continuous. JEE tests this concept by asking you to find the value of a constant that removes the discontinuity — a straightforward 4-mark question if you know the definition.

Both. Functions are introduced in Class 11 (Chapter 2: Relations and Functions) and extended in Class 12 (Chapter 1: Relations and Functions, and Chapter 5: Continuity and Differentiability). JEE Mains integrates concepts from both. Start with Class 11 to build domain/range and types of functions, then move to Class 12 for continuity and advanced limit techniques.