Maclaurin’s Series | √(1 + sin 2x) Expansion | VTU Engineering Mathematics Exam Problem

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   • Maclaurin’s Series Expansion | Important V...  

🎥 Watch Videos:
1️⃣ √(1 + sin 2x) Expansion 👉    • Maclaurin’s Series | √(1 + sin 2x) Expansi...  
2️⃣ √(1 + cos 2x) Expansion 👉    • Maclaurin’s Series | √(1 + cos 2x) Expansi...  
3️⃣ log(1 + cos x) Expansion 👉    • Maclaurin’s Series | log(1 + cos x) Expans...  

📘 Using Maclaurin’s Series | Expansion of √(1 + sin 2x) | Engineering Mathematics

In this video, we prove the Maclaurin series expansion of the expression
√(1 + sin 2x) using standard series formulas.
This problem is frequently asked in Engineering Mathematics exams and is important for understanding series expansion techniques.

🧠 Problem Covered
Using Maclaurin’s series, prove that
√(1 + sin 2x) = 1 + x − x²/2 − x³/6 + x⁴/24

✏️ What You Will Learn
Maclaurin series expansion of sin 2x
Binomial expansion of √(1 + u)
How to simplify and collect terms up to x⁴
Proper exam writing method
How higher order terms are neglected

🎯 Useful For
VTU Engineering students
Semester exams
Series expansion problems
Maclaurin and Taylor series practice
Calculus problem solving

💡 Exam Tip
Always expand trigonometric functions first, then apply binomial expansion, and finally simplify step by step up to the required power of x.

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
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• Module 2 – Power Series expansion, Indeterminate Forms & Multivariable Calculus
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✔ Linear Algebra (Branch-wise)

• 1BMATE101 (EC & EE) / 1BMATC101 (CE)– Module 5
   • Linear Algebra Made Simple – Complete  

• 1BMATM101 (ME) – Module 4
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✔ Most important playlists done to score more marks
✔ High-weightage topics for IA and SEE


⭐ VTU Semester 1 – MUST WATCH Playlists (Score Booster)

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Model QP–I 2025
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M1 – Differential Calculus
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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 ...  

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