# Chapter 03: General Theorem, Intermediate Forms

## What is in the this chapter?

- Rolle's theorem
- Geometrical interpretation of Rolle's theorem
- The mean value theorems
- Another form of mean value theorem
- Increasing and decreasing functions
- Cauchy's mean value theorem
- Extended mean value theorem
- Indeterminate form
- The form $\frac{0}{0}$
- The form $\frac{\infty}{\infty}$
- The form $0\times \infty$ (or $\infty \times 0$)
- The form $\infty-\infty$
- The forms $0^\infty, 1^\infty, \infty^0$
- Use of expansions

### Solutions

- Exercise 3.1 | View Online | Download PDF

- Exercise 3.2 | View Online | Download PDF

- Exercise 3.3 | View Online | Download PDF

We are very thankful to Muhammad Idrees for providing notes of Exercise 3.3

#### Notes by Muhammad Idress

- Exercise 3.3 | View Online | Download PDF

#### Notes by Prof. M. Tanveer

- Exercise 3.1 | View Online | Download PDF

- Exercise 3.3 | View Online | Download PDF