MediumPower & Taylor series

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.5 Power Series, #23 · Calculus · Power & Taylor series

(Proof of the remainder formula when …) (a) At … find

17–24 are about remainders and are about binomials.

(Proof of the remainder formula when $n = 2$ )
(a) At $x = a$ find $R_{2}, R_{2}^{'}, R_{2}^{''}, R_{2}^{'''}$ .
(b) At $x = a$ evaluate $g (x) = (x - a)^{3}$ and $g^{'}, g^{''}, g^{'''}$ .
(c) What rule gives $\frac{R _{2} ( x ) - R _{2} ( a )}{g ( x ) - g ( a )} = \frac{R _{2}^{'} ( c _{1} )}{g ^{'} ( c _{1} )}$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.5 Power Series, #23

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