About the Book

The first crime of mathematicians is that they only give you the definition and properties of limits, but they don't give you procedures and rules to follow for various function structures.
The second crime of mathematicians is that in an exam they ask you how to apply the limit, although they never clearly explain how to use them. You will never see a mathematician who will say we distinguish functions by such structures, here are the procedures that must be followed to find the limit in the structure of a certain structure.
The third crime of mathematicians is that they pretend that uncertainties are something extraordinary and that finding the limit of a function is usually easy and pleasant. Although in fact, the limit was invented just to explore the meaning of functions in difficult places, where using only arithmetic tools it is impossible to find the limit, that is, just to find the limit in uncertainty.
And mathematicians presented such a tool to all mankind, which they called the limit. You will all say yes, we know the limit, because we know the definition of the limit. And I'll tell you no. You only know the definition of the limit. So you have problems with limits, because mathematicians only gave you the definition of the limit, but not all the procedures and rules of the limit.
The damned mathematicians only delivered half of they promised to.
The limit consists of:

1. Limit definitions
2. Limit Properties
3. A set of procedures and rules that describe the use of limits in functions with different structures.

But the damned mathematicians only gave you the definition and properties of limits. But they don't give the most important part describing how to use the limit in different function structures. In fact, it's the mathematicians ' fault that you can't understand calculus.
The limit was deliberately invented in order to increase a function like a microscope where the value of this function cannot be found using only arithmetic tools.
Second, the limit includes a set of procedures and rules that we call tools. Where you have uncertainty in arithmetic - this is a signal to use the limit tools.
By the way, this section of mathematics is called analysis, because in this section you learn to study and analyze functions in depth. You learn procedures and rules that allow you to learn functions in depth. The arithmetic doesn't change. Your procedures and rules change depending on the function you are studying. For each individual function structure, there is a separate procedure and separate rules.
This booklet provides an example of how to distinguish between different function structures and what procedures and rules to apply depending on the function structure.
In fact, studying at the university assumes that you will carefully research all these methods by yourself during your studies. The system implies that you must independently organize your knowledge, independently learn new techniques, and independently invent new research methods.
The task is grandiose.
Yet, it is very stupid one. Because it will take enormous amount of intellectual effort to discover yet one of this techniques. So it is time wise inefficient. Forget about the fact, that they actually don't teach scientific method in Junior year, yet they want you to be able to apply it masterfully to calculus problems. Majority of university instructors are unaware of how learning process is happening, and just expect you to make quantum leaps in your consciousness and magically come up with the solutions to complex problems.
Instead what they should have done, is to be honest with themselves. They should have spent entire semester just teaching scientific method and its applications in calculus discoveries, and then teaching how this method helped to discover tools and techniques. And then teach how to conduct a research and find solutions