Unit 12 Class 11 Math Notes – Limit and Continuity (Punjab Board New Book)
Unit 12 (Chapter 12) Class 11 Math Notes – Limit and Continuity: step-by-step solutions of Exercise 12.1, Exercise 12.2 and Exercise 12.3 for the Punjab Board new book (1st Year). Tap an exercise below to open its PDF solution, then view it online or download it.
This unit is part of our Class 11 maths notes for the Punjab Board new book, where you can open the solutions of the other units.
Exercise Wise Solutions of Unit 12 Class 11 Math
What Each Exercise of Unit 12 Covers
Exercise 12.1 – Limits
Exercise 12.1 has 5 questions on limits of sequences, the limit theorems, factorising and rationalising, trigonometric limits and limits in terms of \(e\).
Exercise 12.2 – Continuity
Exercise 12.2 has 7 questions on left-hand and right-hand limits, continuity of piecewise functions and finding constants that make a function continuous.
Exercise 12.3 – Applications of Limits and Continuity
Exercise 12.3 has 8 questions on applied limits: decay, population, sales, signal strength, stock price, inflation and continuity of a cost function.
Key Formulas of Unit 12 Class 11 Math
- \(\displaystyle\lim_{x\to0}\dfrac{\sin x}{x}=1\)
- \(\displaystyle\lim_{n\to\infty}\left(1+\dfrac1n\right)^n=e\)
- \(\displaystyle\lim_{x\to0}\dfrac{e^x-1}{x}=1\)
- \(\displaystyle\lim_{x\to a}\dfrac{x^n-a^n}{x-a}=na^{n-1}\)
- \(f\) is continuous at \(a\) if \(f(a)\) exists, \(\lim_{x\to a}f(x)\) exists, and the two are equal.
Related Class 11 Math Notes
Continue with Unit 11 Class 11 Math Notes and Unit 13 Class 11 Math Notes, or go back to the Class 11 maths notes hub for all 14 units.
FAQs About Unit 12 Class 11 Math
How many exercises are there in Unit 12?
Unit 12 has three exercises: Exercise 12.1, 12.2 and 12.3.
When is a function discontinuous at a point?
A function is discontinuous at \(x=a\) if \(f(a)\) is not defined, the limit at \(a\) does not exist, or the limit exists but is not equal to \(f(a)\).
Are these notes for the new book?
Yes. These solutions are for the new Class 11 mathematics book by PECTAA (2025 edition onwards), used by the nine BISE Punjab boards: Lahore, Gujranwala, Faisalabad, Multan, Rawalpindi, Sargodha, Sahiwal, Bahawalpur and Dera Ghazi Khan.