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Let our function, f, be infinitely differentiable in the point x= 0 with |f (n) (0)|

Let our function, f, be infinitely differentiable in the point x= 0 with |f⁽ⁿ⁾(0)| <= 2ⁿ for all n. Show that the sequence of Taylor polynomials is pointwise convergent. Is it also uniformly convergent?

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