MediumPower & Taylor series

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.5 Power Series, #24 · Calculus · Power & Taylor series

All derivatives of … are zero at …, including

17–24 are about remainders and are about binomials.

All derivatives of $f (x) = e^{- 1/ x^{2}}$ are zero at $x = 0$ , including $f (0) = 0$ . What is $f (1)$ ? What is the Taylor series around $x = 0$ ? What is the radius of convergence? Where does the series converge to $f (x)$ ? For $x = 1$ and $n = 1$ what is the remainder estimate in (2)?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.5 Power Series, #24

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