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eMath 7: Derivatives

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The ebooks are structured so that you will learn all concepts in a logical order and it is meant to be studied from beginning to end. The theory parts are short and concise and at the end of each lesson, you will find a page with assignments. The assignments can be solved directly in the book.
You can easily write mathematics on the computer with the 4f Studio math tools, as well as insert pictures, embedded elements and graphs to support your studies and solutions. When your are finished, you can let the computer automatically check your assignments. The automatic checker sends each step in the derivation to an automatic theorem prover. If each step in the derivation is proved correct, the derivation is correct. The checker warns when it was not able to prove a derivation step correct, so that you can inspect the step, see your mistakes easily and correct them. See 4f Checker for more details.
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  • Numerical and symbolical calculator

Overview: This book introduces the basic notions of calculus: continuity, limits, and derivatives. It shows how to compute the derivative of a function. It applies this to describe the behaviour of functions, and to find extreme values of functions. Additionally, it includes a chapter on how to work with rational expressions.

Table of contents:

1 Preface
2 Rational Expressions
2.1 Rational Expressions
2.2 Rational Equations
2.3 Rational Inequalities
3 Continuity and Limits
3.1 The Definition of Continuity and Limit
3.2 Calculating Limits
3.3 Piecewise Defined Functions
3.4 Results Related to Continuous Functions
4 Derivative
4.1 Derivative And Difference Quotient
4.2 Differentiation Rules
4.3 Tangents and Normals
5 The Behavior of a Function
5.1 The Monotonicity of a Function
5.2 Derivative and Monotonicity
5.3 Local Extreme Values
5.4 The Greatest and Smallest Value of a Function