IIT JAM Physics 2026| Taylor Series Expansion Problem Explained Step-by-Step#IITJAM2026#TaylorSeries

In this video, we solve and explain an important Taylor Series expansion problem from IIT JAM Physics 2026. Taylor series is a powerful mathematical tool widely used in physics, engineering, and applied mathematics to approximate complicated functions using polynomial expressions around a specific point. In many competitive examinations like IIT JAM Physics, CSIR NET Physics, JEST, TIFR GS, and GATE Physics, Taylor series plays an important role in simplifying physical expressions, deriving approximations, and solving problems involving small quantities. In this lecture, we carefully analyze the Taylor expansion problem step by step and demonstrate how to expand a function about a point using derivatives. We also discuss how physicists often use small quantity approximations such as when 𝑥 ≪ 1 x≪1, which is extremely common in exam problems. The Taylor series expansion of a function 𝑓 ( 𝑥 ) f(x) about a point 𝑎 a is given by: f(x) = f(a) + (x − a)f'(a) + (x − a)²/2! f''(a) + (x − a)³/3! f'''(a) + ... When the expansion is taken around a = 0, it becomes the Maclaurin Series, which is frequently used in physics calculations. Key concepts explained in this video include: • Concept of Taylor Series and Maclaurin Series • Step-by-step method to expand functions using derivatives • Application of Taylor expansion in physics problems • Understanding small parameter approximations • Important standard expansions used in exams • Tricks for solving IIT JAM Physics questions quickly Some important standard expansions that students must remember include: e^x ≈ 1 + x + x²/2! + x³/3! + ... sin x ≈ x − x³/3! + x⁵/5! − ... cos x ≈ 1 − x²/2! + x⁴/4! − ... ln(1 + x) ≈ x − x²/2 + x³/3 − ... Understanding these expansions helps simplify many physics problems, especially in mechanics, quantum mechanics, optics, and statistical physics. This video is part of our IIT JAM Physics 2026 Complete Solution Series, where we solve questions from the exam paper and explain the concepts in a clear and structured way. The objective is to help students strengthen their mathematical tools that are essential for solving advanced physics problems. This lecture will be especially useful for students preparing for: IIT JAM Physics CSIR NET Physics JEST Physics TIFR GS Physics GATE Physics MSc Physics Entrance Examinations At Dr. Sourav Sir’s Classes, we focus on conceptual clarity, mathematical techniques, and exam-oriented problem solving so that students can build strong foundations required for competitive exams. For academic guidance and coaching support: Website: www.souravsirclasses.com Contact: 9836793076