Master Newton–Raphson from S. M. Yusuf, Calculus with Analytic Geometry, Exercise 2.4—complete, step-by-step solutions with theory, intuition, and exam shortcuts. We cover ✅ Deriving the NR formula ✅ How to pick a good initial guess (and when NR fails) ✅ Absolute vs relative error stopping rules ✅ All question types from Ex 2.4: single root, repeated root behaviour, and ✅ accuracy to n-decimal places ⏱ Timestamps 00:00 Intro & Roadmap 01:02 NR Formula & Geometric Idea (tangent method) 06:26 Ex 2.4 Q 1 16:40 Ex 2.4 Q 2 21:49 Ex 2.4 Q 3 28:55 Ex 2.4 Q 4 32:10 Ex 2.4 Q 5 35:20 Geometric interpretation 41:43 Ex 2.4 Q 5 47:39 END 📚 Reference (verified): S. M. Yusuf, Calculus with Analytic Geometry, Exercise 2.4 — Newton–Raphson Method. (General convergence remarks are standard numerical analysis practice; not tied to a single example in Yusuf.📚 Calculus with Analytic Geometry by S. M. Yusuf – Chapter 2: Derivatives – Exercise 2.4 🎯 Perfect for: BSc/BS Mathematics, Engineering students, and anyone following S. M. Yusuf – Calculus with Analytic Geometry in Pakistani universities like Punjab University, Karachi University, Peshawar University, and Quaid-e-Azam University. 📎 Download Lecture Notes PDF https://drive.google.com/file/d/1U-To... 🔔 Subscribe to MforMathodology for more detailed math lectures and past paper solutions! 📢 Share with friends preparing for Calculus exams! #Calculus #SMYusuf #Derivative #PakistaniUniversities #BScMaths #FirstPrinciple #MforMathodology #MathTutorial #AnalyticGeometry #exercise2_1 #Discontinuity #SMYusuf #exercise1_3 #Calculus #Limit #SMYusuf #Exercise1_2 #MathsWithMforMathodology #analyticgeometry #Calculus #Continuity #SMYusuf #Exercise1_3 #ContinuousFunction #MforMathodology #Calculus #SMYusuf #DerivativeApplications #Physics #Engineering #Economics #PakistaniUniversities #MarginalFunctions #RocketVelocity #MforMathodology #Calculus #SMYusuf #DerivativeRules #PakistaniUniversities #PowerRule #ProductRule #QuotientRule #ChainRule #BScMaths Agar maza aaya ho, toh like, share, subscribe aur comment karna mat bhoolna: "Next kis chapter ki video chahiye?" 💬👇