Find Real Root of 3x = cos x + 1 using Newton–Raphson Method | VTU Numerical Methods

Learn Newton–Raphson Method with an important VTU Numerical Methods problem solved step-by-step for nonlinear equations. Perfect for understanding iterative root-finding techniques with faster convergence. ━━━━━━━━━━━━━━━━━━━━━ 📘 Subject Mapping: 📚 Newton–Raphson Method for: • 1BMATS201 (Module 1) • 1BMATE201 (Module 3) • 1BMATC201 (Module 4) • 1BMATM201 (Module 4) ━━━━━━━━━━━━━━━━━━━━━ 📌 Exact Question (with Timeline): ⏱️ 0:00 → Find the real root of the equation 3x = cos x + 1 by Newton–Raphson Method. ━━━━━━━━━━━━━━━━━━━━━ 🎯 Learning Points: ✔ Newton–Raphson Method step-by-step ✔ Forming nonlinear equation correctly ✔ Finding f(x) and f′(x) ✔ Iterative root approximation ✔ Faster convergence technique ✔ VTU exam solving strategy ━━━━━━━━━━━━━━━━━━━━━ 📚 Watch Next: 1️⃣ Newton–Raphson Method (x log₁₀x = 1.2)    • Find Real Root of x log₁₀x = 1.2 using New...   2️⃣ Newton–Raphson Method (x e^x = 2)    • Find Real Root of x e^x = 2 using Newton–R...   3️⃣ Full Numerical Methods Playlist    • 1BMATS101 Module 1 | Numerical Methods | B...   ━━━━━━━━━━━━━━━━━━━━━ 📘 Module Playlist (Start to Finish): ▶️ VTU Numerical Methods Problems Solved | Bisection, Regula Falsi & Newton–Raphson    • 1BMATS101 Module 1 | Numerical Methods | B...   ━━━━━━━━━━━━━━━━━━━━━ 📙 More Practice / Related Method: 1️⃣ Regula Falsi Method    • Regula Falsi Method: Solve 3x - 1 = cos x ...   2️⃣ Bisection Method    • Find Real Root of x³ − 7x + 5 = 0 using Bi...   ━━━━━━━━━━━━━━━━━━━━━ 🚀 Next Step: Continue with logarithmic and exponential root-finding problems. 📌 Don’t stop here: Practice Newton–Raphson iterations regularly for better speed and accuracy. ━━━━━━━━━━━━━━━━━━━━━ 👉 Follow VTU Maths with Muheeb (Mathematics Tutor) on WhatsApp https://whatsapp.com/channel/0029Vb6c... 👉 Get all VTU Maths updates and video links on Telegram https://t.me/vtumathswithmathematicst... 💎 Support Us: Join our channel and get access to exclusive perks 👇    / @officialmathematicstutor   ━━━━━━━━━━━━━━━━━━━━━ 📙 All 1BMATS201 Playlists: M1:    • 1BMATS201 Module-1: Introduction to Numeri...   M2:    • 1BMATS201 Module-2: Numerical solutions fo...   M3:    • 1BMATS201 Module-3: Interpolation   M4:    • 1BMATS201 Module-4: Differential Equations...   M5:    • 1BMATS201 Module-5: Numerical Integration ...   ━━━━━━━━━━━━━━━━━━━━━ 📙 All 1BMATE201 Playlists: M1:    • 1BMATE201 Module 1 | Double Integrals, Tri...   M2:    • Vector Calculus & Applications | VTU 1BMAT...   M3:    • 1BMATE201 Module 3 | Numerical Methods I |...   M4:    • 1BMATE201 Module 4 | Numerical Methods II ...   M5:    • 1BMATE201 Module-5: Laplace transforms   ━━━━━━━━━━━━━━━━━━━━━ ⭐ Best 7 Hashtags: #NewtonRaphsonMethod #NumericalMethods #VTUMaths #1BMATS201 #EngineeringMathematics #RootFinding #MathsMadeEasy