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(3) (a) Why does it not make sense to find the Taylor series of f(x) =...

(3)

(a) Why does it not make sense to find the Taylor series of f(x) = √3 x at a = 0?

(b) Without calculating the Taylor series, explain why the radius of convergence for the Taylor series of f(x) = 1 (x−3)(x+7) at a = 0 cannot be more than 3. (You may assume the Taylor series is equal to the function when it converges.)

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