Question

got the first one but the last 4 are giving me trouble.

i) Calculate the first four Taylor polynomials Po(r), P(), P2(), P3(1) ii) Sketch the function together with the first four Taylor polynomials Po(x), P (r), P(x), P3(1) around the basis point iii) Find the general form of the n-th Taylor polynomials P,(x) and write down the Taylor series for the function about the basis point a iv) Calculate the interval of convergence of the Taylor series (calculate first the radius of convergence and then investigate carefully the endpoints of the interval) a) f(x) == about a 3; 7T b) g(x) = sin(r) about a = 1 c) h(a)2-4 about a = 4; = d) k(x) 2re" about a = 0; e) () r(In(r))-1) about a = e.

Answer 1

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