Category archives: Differential Calculus

Limit of Functions of a Real Variable Summary: This class thoroughly reviews the formal definition of limits of functions of a real variable, and from this, the main properties that lead to the algebra of limits are demonstrated. Learning Objectives: At the end of this class, the student will be…

Solved Problems: Finite Limits Summary: This class offers solved problems on the calculation of finite limits, accompanied by a video tutorial. Students are guided to solve the problems and compare their results with the provided solutions. Key techniques such as rationalization and the use of graphs are highlighted, encouraging different…

The Squeeze Theorem for Calculating Limits Summary: This class presents the Squeeze Theorem, a key tool in calculus for evaluating difficult limits using simpler functions that bound from above and below. It offers a graphical explanation and a formal proof, followed by practical examples. The goal is for students to…

One-Sided Limits: Definitions, Development, and Exercises Summary: This post explains one-sided and bilateral limits in calculus, showing how they are defined and applied both intuitively and formally. Graphical and algebraic examples are presented, the conditions for using limit algebra in these cases are discussed, and solved exercises are included to…

Limit at Infinity: Definitions and Examples Summary: This class will cover limits at infinity, describing the behavior of as tends to infinity. Basic limits like and are explained, along with algebraic properties similar to those of finite limits. Learning Objectives: By the end of this class, the student will be…

Infinite Limits and Divergence Summary: In this class, we will address infinite limits and the different types of divergence in limits, exploring fundamental concepts to understand how certain functions do not converge to a defined real value. We will review disparate lateral limits, infinitely oscillating functions, and situations where limits…

Asymptotes, Limits, and Graphing Techniques Summary: In this class, we address the concepts of asymptotes and dominant terms in the analysis of functions. We explore horizontal asymptotes, which describe the behavior of a function as tends to infinity; vertical asymptotes, which indicate infinite limits when approaches certain values; and oblique…

Limit and Continuity Summary: This class addresses the relationship between the limit and the continuity of a function, starting with an intuitive and formal explanation of the term. Continuity at a point and in a set is explored, detailing the necessary conditions for a function to be continuous. The algebraic…

The Derivative as the Limit of a Function Abstract: In this lesson, we will explore the concept of the derivative as the mathematical tool to analyze changes in functions. Starting from the slope of a secant line, and taking the limit as the points get closer, we will define the…

Derivatives of Polynomials, Trigonometric and Logarithmic Functions The derivative is a central tool in differential calculus, with fundamental applications in science, engineering, and economics. This article offers a progressive guide to mastering the differentiation of functions, from polynomials to trigonometric and logarithmic functions. Through demonstrations and concrete examples, it aims…