Can you solve these? Thank you! Page <2of 2ZOOM+III. Higher Degree ApproximationsIfwe continue to raise the degree of our approximation we can continue to add conditions. For– a) + C(x – a)² + D(x – a)³ can satisfyinstance a third degree approximation P(x) = A + B (x -conditions (i), (ii) and (iii) as well as a fourth condition (iv) P''(a) = f''(a)13) Find a third degree approximation of f (x) = sin x at x = -6.14) Derive formulas for A, B, C, and D for any third degree approximation of a function f(x)centered at a.In general we would like to find an nth-degree polynomialT, (x) %3D со + c1 (х — а) + с2(х — а)2 + с3(х — а)3 + ..+Cn(x – a)"where T, and its first n derivatives have the same value at x = a as f and its first n derivatives.T, (a) = f(®)(a)(k)T,(a) = f(a), Th(a) = f'(a), T"(a) = f"(a)T(^) (a) = f(n) (a)......This polynomial is called the nth-degree Taylor polynomial of f centered at a. These will beexplored in further detail in Math 1C. For now we will just take a look at how these increasingly higherdegree approximations relate to each other and how they provide increasingly more accurateapproximations.15) Find the 2nd, 4th, 6"™, and 8h degree Taylor polynomials for f(x)= cos x centered at x = 0.16) Use graph paper to provide a detailed and accurate graph of f, T2, T4, T6, and Tg on the samegraph with a domain of [-7, 1].17) In questions (12) and (14) you found formulas for the coefficients of a second degree and a thirddegree approximation (These are T2(x) and T3(x) respectively). Come up with a conjecture for theformula for the kth coefficient of T (x).п18) Can you prove the conjecture you proposed in (17)?

Name: Can you solve these? Thank you! Page <2of 2ZOOM+III. Higher Degree App
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Description: Can you solve these? Thank you! Page <2of 2ZOOM+III. Higher Degree ApproximationsIfwe continue to raise the degree of our approximation we can continue to add conditions. For– a) + C(x – a)² + D(x – a)³ can satisfyinstance a third degree approximatio