How to Find the Domain & Range of Multivariable Functions (Calculus 3 Lesson 39) ➡️ Download my FREE Multivariable Function Cheat Sheets: 🖥️ Membership Site (community & bonus content): 🌐 My Website: ⭐️ Support Me on Patreon: In this video you will learn about multivariable functions, or functions of several independent variables. You’ll be introduced to their notation, what defines a multivariable function, and what their graphs look like. Additionally, we talk about combinations of multivariable functions and what a composite function may look like. Finally, you’ll learn how to find the domain and range of multivariable function as well as graph the domain. We also briefly talk about how to graph multivariable functions by recognizing special surfaces, but the actual techniques have been learned in previous lessons (planes, cylinders, quadric surfaces), so we will not look at any examples. This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture! Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 What is a Multivariable Function? 5:51 Single Variable vs Multivariable Functions 12:49 Definition of Multivariable Functions 17:09 Example: Evaluating Multivariable Functions 19:36 Combinations & Composite Multivariable Functions 23:05 How to Find Domain & Range 30:02 Example: Domain & Range of 2xy/(x-y) 32:28 Example: Domain & Range of √(9-x²-y²) 36:32 Graphing Domain of Multivariable Functions 42:13 Example: Graph Domain of ln(y-x)/√(x-y+2) 46:56 Example: Graph Domain of √(25-x²-y²-z²) 50:18 Graphing Multivariable Functions Corrections: 0:48 I mistakenly wrote the formula for the volume of a right circular cylinder, not a cone. If you divide the height h by 3, then the formula would be correct. This ultimately does not change the point I was making at this point in the video. Both formulas are examples of multivariable functions. 📝 Examples Video: ⏩ Next Lesson: 📺 Calculus 3 Playlist: 📺 Calculus 2 Playlist: 📺 Calculus 1 Playlist: ⚡️Math Products I Recommend⚡️ Graphing Calculator: Non-Graphing Calculator: Financial Calculator: Graphing Paper: College Rule Paper: My Favorite Pencil: My Favorite Erasers: Calculus Workbook: ⚡️Textbooks I Use⚡️ Calculus 1 & 2: Calculus 3: Financial Mathematics: Algebra: ⚡️My Recording Equipment⚡️ iPad Air: Apple Pencil (Gen 2): Tablet Desk Stand: External Hardrive: (Commissions earned on qualifying purchases) Follow me on Social Media! Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! - Josh from JK Mathematics #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.