The goal of this textbook is to help the learners learn calculus intelligently for solving a wide variety of mathematical and physical problems. The talent of teaching, Mark Van Doren said, is the talent of supplementary funding. I have tried to write a book that assists students in learning calculus book both for its real-world influence and its astounding attractiveness. In this textbook, I purpose to take to the student a sense of the helpfulness of calculus and mature mechanical capability, but I also endeavor to give some indebtedness for the inherent attractiveness of the subject that means in mathematics. From the writers of Calculus certainly experienced a sense of achievement when he made his great findings. The importance is on sympathetic ideas. The Regulation of three has been extended to become the Regulation of four by stressing the oral, or expressive, point of view as well. In writing the textbook my premise has been that it is possible to achieve conceptual understanding and still retain the best traditions of old-style calculus. Finally, this textbook contains four chapters. The first chapter about Inverse Function, the 2nd chapter is about techniques of integration, the 3rd chapter is about indeterminate forms, improper integral and Taylor’s formula and the 4th chapter are about sequences of function. All activities and exercises are given in detail for each chapter for the readers.