Limits of Functions — Single-Variable Calculus

Limits form the conceptual entry point into calculus. This course focuses on the idea of approaching a value — what it means for a function to tend toward a limit, and how to analyze this behavior rigorously. We examine left-hand and right-hand limits, infinite limits, and limits at infinity. You'll also learn to handle indeterminate forms and use algebraic techniques to simplify complex limit expressions. By the end of the course, you’ll have a clear grasp of how limits underpin both continuity and derivatives, and why they matter.

139

19 hrs

$ 8.58

Payment required for enrolment

Enrolment valid for 12 months

This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.

[FUTA, Akure] MTS 102: Introductory Mathematics II

This learning track is structured for first-year students at the Federal University of Technology, Akure (FUTA) and mirrors the standard second-semester coverage of elementary calculus. It begins with single-variable functions and their graphs, then walks learners through limits, continuity, differentiation techniques, and curve sketching—just as covered in the official MTS 102 outline. You’ll also explore anti-derivatives and integration, learning both the techniques and how to apply them to solve practical problems in science and engineering contexts. Everything is broken down into short, focused video lessons that keep things clear and manageable, especially for students who might be engaging this content for the first time. If you're not a FUTA student but need to build a solid foundation in these same topics, this track can serve you just as well. The structure and explanations are universal, ensuring that learners with similar academic goals can benefit fully.

[UNILAG, Akoka] MTH 102: Elementary Mathematics II

This learning track is designed to guide first-year students at the University of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners. The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior. Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.

[OAU, Ife] MTH 201: Mathematical Methods I

Comprehensive treatise of advanced calculus covering limits, continuity and differentiability, infinite sequences and series, partial differentiation, numerical methods and ordinary differential equations. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Course Chapters

Introduction

Meaning of the limits of a real-valued functions - graphical illustrations and formal (epsilon-delta) definitions.

Chapter lessons

1.Informal definition19:20

An informal definition of the limit of real-valued functions.

2.Formal definition17:26

A formal (rigorous) definition of the limit of real-valued functions.

Proving Finite Limits

How to prove that a given finite limit as x approaches a finite value is correct, using the formal or epsilon-delta definition.

Chapter lessons

1.Worked examples (1)13:51