362/1000 | Taylor Series Expansion of x/(1+x) Around x = 0 | Maclaurin Series Formula | Calculus

362/1000 | Taylor Series Expansion of x/(1+x) Around x = 0 | Maclaurin Series Formula | GATE Calculus
Notes- https://youtube.com/shorts/hzqblMd7aWY?si=nvGCVnVz8RoOxpoa
Taylor Series Playlist - https://youtube.com/playlist?list=PLT2xRiy9TL2gexU0ILSnrHXQYcrnB57zS&si=FcUheJCAlg9dli-5
Description:_
Find the Taylor Series of f(x) = x/(1+x) around x = 0! 🚀 This 1-minute concept is a favorite in GATE, JEE, and BSc exams:
00:00 Taylor Series
00:20 The Taylor series expansion for the function f(x) = x/(1+x) around x = 0
00:40 Formula of Taylor Series expansion around x = a
00:50 Maclaurin series formula

Perfect for GATE, ESE, JEE, BTech, BSc, and Class 12 students. Shortcut: Use geometric series 1/(1+x) = 1 - x + x² - x³ + ... for |x| less than 1. Multiply by x to get x/(1+x) = x - x² + x³ - x⁴ + ...

You can also use successive differentiation. f(0) = 0, f'(x) = 1/(1+x)² gives f'(0) = 1, f''(0) = -2, f'''(0) = 6. Same result.

Subscribe for more Taylor Series, Maclaurin Series, and Engineering Mathematics shorts! 📚💻 Series expansion of rational functions appears in Calculus, Sequences & Series, and Numerical Methods. Like, share, and comment with your doubts!

Some key topics covered in this video include:
- Taylor Series at x = 0
- Maclaurin Series of x/(1+x)
- Geometric Series Application
- Rational Function Expansion
- Successive Differentiation Method
- Engineering Mathematics

_Hashtags:_ #TaylorSeries #MaclaurinSeries #Calculus #EngineeringMathematics #SeriesExpansion #RationalFunction #MathShorts #GATE #JEE #BTech #BSc #Class12 #MathExplained #MathTutorial #GeometricSeries

_Most searching keywords:_ Taylor Series, Maclaurin Series, Taylor Series of x/1+x, Maclaurin Expansion x/1+x, Series Expansion, Calculus, Rational Function Series, Geometric Series Formula, Engineering Mathematics, GATE, JEE, BTech, BSc, Class 12, Function Approximation, Sequences and Series

Видео 362/1000 | Taylor Series Expansion of x/(1+x) Around x = 0 | Maclaurin Series Formula | Calculus канала GAURAV Kumawat (Gk)