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  • 06:1306:13, 17 December 2023 diff hist +546 N Science:Math Exam Resources/Courses/MATH100/December 2016/Question 13 (a)/Solution 2Created page with "We know (or can calculate) that the Taylor expansion of <math>\sin(x)</math> centred at <math>x = 0</math> is :<math> \sin(x) = x - \frac{x^3}{3!} + \cdots. </math> Hence the Taylor expansion of <math>f(x) = (x+1) \sin(x)</math> centred at <math>x = 0</math> is :<math> (x+1)\sin(x) = (x+1)\left(x - \frac{x^3}{3!} + \cdots\right) = x^2 - \frac{x^4}{3!} + x - \frac{x^3}{3!} + \cdots. </math> Discarding the terms of degree higher than 3, we obtain the third degree Taylor po..." current

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