Let f(x) = sin(x). Let p(x), P3(x), p5(x) be the Taylor polynomials of degree 1, 3,...

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Let f(x) = sin(x). Let p₁(x), P3(x), p5(x) be the Taylor polynomials of degree 1, 3, and 5 for f(x) and the point of approximation 0. 1. What are p₁(x), P3(x), p5(x)? 2. What are p2n-1(x) and p2n(x) for integer n ≥ 1? 3. Compare the values of f(x), p₁(x), p3(x), p5(x) for x = ±½‚±‚±7. 哥哥, Let p2n-1(x) be the formula that you have computed large should the degree 2n - 1 be chosen so that |sin(x) - P2n-1(x)| ≤ 0.001 πT for all - ≤ x ≤? Check your result by evaluating the resulting p2n-1 (Hint: Taylor's remainder theorem.) -1(x) at x = 7/2. How Let f(x) = sin(x). Let p₁(x), P3(x), p5(x) be the Taylor polynomials of degree 1, 3, and 5 for f(x) and the point of approximation 0. 1. What are p₁(x), P3(x), p5(x)? 2. What are p2n-1(x) and p2n(x) for integer n ≥ 1? 3. Compare the values of f(x), p₁(x), p3(x), p5(x) for x = ±½‚±‚±7. 哥哥, Let p2n-1(x) be the formula that you have computed large should the degree 2n - 1 be chosen so that |sin(x) - P2n-1(x)| ≤ 0.001 πT for all - ≤ x ≤? Check your result by evaluating the resulting p2n-1 (Hint: Taylor's remainder theorem.) -1(x) at x = 7/2. How