L'Hopital's Rule | Calculus 2 Lesson 16 - JK Math

How to Use L’Hopital’s Rule For Limits of Indeterminate Forms (Calculus 2 Lesson 16) In this video we learn about how to evaluate limits involving indeterminate forms of 0/0 or ∞/∞ using L’Hopital’s Rule. This rule/technique allows us to evaluate limits in these indeterminate forms by taking the derivative of the numerator and denominator of the function in the limit to simplify it and make its evaluation possible. We also look at a few other indeterminate forms for limits that can be manipulated into a form where L’Hopital’s Rule applies. We go through several examples and explain the evaluation process step-by-step. 🖥️ Join My Membership Site: https://www.jkmathematics.com/plus This series is designed to help students understand the concepts of Calculus 2 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 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 Review of Indeterminate Forms 6:40 L’Hopital’s Rule 8:23 Example - x/e^x as x approaches ∞ 10:58 Example - (e^(2x)-1)/x as x approaches 0 13:31 Example - (x^2-9)/(x-3) as x approaches 3 15:12 Example - (5x^2-2)/(2x^2+1) as x approaches ∞ 17:05 Example - e^x/x^2 as x approaches ∞ 21:30 Other Indeterminate Forms 22:45 Example - e^(-x)*sqrt(x) as x approaches ∞ 27:41 Example - (sin(x))^x as x approaches 0 from the right 38:53 Outro 📝 Examples Video:    • L'Hopital's Rule Examples | Calculus 2 - J...   ⏩ Next Lesson:    • Improper Integrals | Calculus 2 Lesson 17 ...   📺 Calculus 2 Playlist:    • Calculus 2   📺 Calculus 1 Playlist:    • Calculus 1   🌐 Visit My Website: https://www.jkmathematics.com ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://amzn.to/3XuUcB9 Non-Graphing Calculator: https://amzn.to/46hHJ7E Financial Calculator: https://amzn.to/3CRe9s4 Graphing Paper: https://amzn.to/46mAfAr College Rule Paper: https://amzn.to/3NOJaTN My Favorite Pencil: https://amzn.to/3NOFMIB My Favorite Erasers: https://amzn.to/3PumUQB Calculus Workbook: https://amzn.to/3r8SnNP ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://amzn.to/3PzfI5F Calculus 3: https://amzn.to/46rSy76 Financial Mathematics: https://amzn.to/3ppIVW0 ⚡️My Recording Equipment⚡️ iPad Air: https://amzn.to/3phEug1 Apple Pencil (Gen 2): https://amzn.to/3Nl45MM Tablet Desk Stand: https://amzn.to/4420rPh External Hardrive: https://amzn.to/44pkEyh (Commissions earned on qualifying purchases) Find me on social media: Facebook:   / jkmathematics   Twitter:   / jk_mathematics   Instagram: @jk_mathematics 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 Math #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.