Indeterminate Forms (1^∞) | Evaluate lim (x→0) [(a^x + b^x + c^x)/3]^(1/x) | VTU Maths

▶️ Full Playlist 👉    • Indeterminate Forms (1^∞) – Most Important...   🎥 Videos 1️⃣    • Indeterminate Forms (1^∞) | Evaluate lim (...   2️⃣    • Indeterminate Forms (1^∞) | Evaluate lim (...   3️⃣    • Indeterminate Forms (1^∞) | Evaluate lim (...   4️⃣    • Indeterminate Forms (1^∞) | Evaluate lim (...   5️⃣    • Indeterminate Forms (1^∞) | Evaluate lim (...   6️⃣    • Indeterminate Forms (1^∞) | Evaluate lim (...   📘 Indeterminate Forms – Evaluate the Limit In this video, we evaluate the limit lim (x→0) [(a^x + b^x + c^x) / 3]^(1/x) As x approaches zero, each exponential term a^x, b^x, and c^x tends to 1. Hence, the given expression reduces to the indeterminate form 1^∞. To evaluate this limit correctly, we use the logarithmic method by taking the natural logarithm on both sides. This converts the power into a product, allowing us to simplify the expression using standard limits and L’Hospital’s Rule. After careful simplification, the limit evaluates to the geometric mean of a, b, and c. ✅ Final Answer: (abc)^(1/3) 🎯 Why this problem is important: • Frequently asked in Engineering Mathematics exams • Tests understanding of indeterminate forms • Useful for VTU, GATE, and university examinations • Strengthens concepts of logarithmic limits and L’Hospital’s Rule This video is useful for: • VTU Engineering Mathematics students • First-year calculus preparation • Quick revision before exams 🎓 Best suited for • VTU Semester 1 students • Exam-oriented derivation practice • Quick revision before IA and SEE 📚 Syllabus Mapping (VTU) • 1BMATE101 (EC & EE) Module 2 – Module-2: Power series Expansions, indeterminate forms and multivariable calculus • 1BMATC101 (CE) Module 1 – Module-2: Power series Expansions, indeterminate forms and multivariable calculus. • 1BMATM101 (ME) Module 1 – Module-2: Series Expansions, indeterminate forms and multivariable calculus. • BMATS101 / BMATE101 / BMATC101 / BMATM101 Module 2 – Common Calculus Topics (2022 scheme) ⭐🆕 Most Important VTU Playlists to Score More Marks (2025 Scheme) ✔ Common Modules -1BMATE101 (EC & EE) / 1BMATC101 (CE)/1BMATM101 (ME) • Module 1 – Differential Calculus / Polar Curves and Curvature    • Module 1 Differential Calculus | Polar Cur...   • Module 2 – Power Series expansion, Indeterminate Forms & Multivariable Calculus    • Partial Differentiation | Multivariable Ca...   ✔ Linear Algebra (Branch-wise) • 1BMATE101 (EC & EE) / 1BMATC101 (CE)– Module 5    • Linear Algebra Made Simple | Rank, Consist...   • 1BMATM101 (ME) – Module 4    • Linear Algebra Made Simple | Rank, Consist...   ✔ Most important playlists done to score more marks ✔ High-weightage topics for IA and SEE ⭐ VTU Semester 1 – MUST WATCH Playlists (Score Booster) 🔹 1BMATE101 (TOP PRIORITY) Model QP–I 2025    • VTU Model Question Paper–I 2025 | 1BMATE10...   M1 – Differential Calculus    • Differential Calculus | VTU 1BMATE101 – Mo...   M2 – Multivariable Calculus    • Power Series, Indeterminate Forms & Multiv...   M3 – ODE    • Ordinary Differential Equations (ODE) | VT...   M4 – Higher Order ODE    • Higher-Order Ordinary Differential Equatio...   M5 – Linear Algebra    • Linear Algebra | VTU 1BMATE101 – Module 5 ...   🔹 1BMATC101 M1    • Polar Curves and Curvature | VTU 1BMATC101...   M2    • Series Expansion, Indeterminate Forms & Mu...   M3    • Ordinary Differential Equations of First O...   M4    • Ordinary Differential Equations of Higher ...   M5    • Linear Algebra | VTU 1BMATC101 – Module 5 ...   🔹 1BMATM101 M1    • Polar Curves and Curvature | VTU 1BMATM101...   M2    • Series Expansion, Indeterminate Forms & Mu...   M3    • Ordinary Differential Equations of First O...   M4    • Linear Algebra | VTU 1BMATM101 – Module 4 ...   ✔ Follow in order to score more marks 👉 WhatsApp: https://whatsapp.com/channel/0029Vb6c... 👉 Telegram: https://t.me/VTUMathsWithMuheeb 💎 Support Us    / @officialmathematicstutor   #LHospitalsRule #LHopitalRule #IndeterminateForms #Limits #Calculus #EngineeringMathematics #VTUMaths