# Chapter 01: Real Numbers, Limits and Continuity

Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN.

The notes of this chapter is written by Prof. Prof. Muhammad Farooq, Punjab College, Sargodha.

### Contents and summary

**Articles of Exercise 1.1**- Rational numbers, Irrational numbers, Real numbers, Complex numbers
- Properties of real numbers, Order properties of $\mathbb{R}$
- Absolute value or modules of a $\mathbb{R}$
- The completeness property of $\mathbb{R}$
- Upper bound, lower bound
- Real line, Interval
- Working rule for the solution of inequality
- Binary relation (B.R), Domain of B.R, Range of B.R
- Function, Onto or surjective funiton, (1-1) Function, Bijective Function
- Real valued function, Image of a function, Bracket function

**Articles of Exercise 1.2**- Finite limit at a finite point
- Left hand limit
- Right hand limit

**Articles of Exercise 1.3**- Continuity

### Notes by Prof M. Farooq

- Articles of Exercise 1.1 | View Online | Download PDF

- Solution of Exercise 1.1 | View Online | Download PDF

- Articles of Exercise 1.2 | View Online | Download PDF

- Solution of Exercise 1.2 | View Online | Download PDF

- Solution of Exercise 1.3 | View Online | Download PDF

### Notes by Prof M. Tanveer

- Exercise 1.1 | View Online | Download PDF

- Exercise 1.2 | View Online | Download PDF

- Exercise 1.3 | View Online | Download PDF

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- by Dr. Atiq ur Rehman