Consider the function f : R→ R, with f(x) cos x for all x E R. For any nЄN, let Tn be the Taylor polynomial of f around 0, of order n. = ex (a) Determine the polynomial T2(x). (b) Use Taylor's approximation theorem to estimate how well T₂ (0.1) approximates f(0.1). (Any upper bound on |T₂(0.1) – ƒ(0.1)| is acceptable, as long as it follows from a correct application of Taylor's theorem and does not involve any unknowns.)

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