Let f(x) = Vx. Which of the following is the Taylor polynomial of degree 1 for f(x) centred at a = 1, T1(x)? (Hint: Use the formula for T1(x) in terms of f(a) and f'(a).) O a. T1(x) = x - 1 O b. T(x) = (x – 1) O c. T1(x) = 1 O d. T(x) = 1+ (x – 1)
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- calculate the Taylor polynomials T2 and T3 centered at x = a for the given function and value of a. f (x) = sin x, a = 0calculate the Taylor polynomials T2 and T3 centered at x = a for the given function and value of a. f (x) = tan x, a = 0Let f(x) = ln(3-x). (a) Find the 2nd order Taylor polynomial for f(x) centered at x = 2. (b) Use T/(x; 2) to approximate In (0.9). Round to 4 decimal places. (c) If |x-2] ≤ 0.1, find a "reasonable" upper bound on error when using T²(x; 2) to estimate f(x). Round to 4 decimal places past the leading 0s.
- Calculate the Taylor polynomial T3 centered at x = a for the given function and values of a andEstimate the accuracy of the 3th degree Taylor approximation, f(x) ≈T3(x), centered at x = a onthe given interval. 2) f(x) = ln(1 + 2x), a = 1, and [0.5,1.5]Let f(x) = 1/(3-2x). (a) Find the 2nd order Taylor polynomial for f(x) centered at x = 1. (b) Use T²/(x; 1) to approximate 1/3. Round to 4 decimal places. (c) If |x-1] ≤ 0.1, find a "reasonable" upper bound on error when using T²(x; 1) to estimate f(x). Round to 4 decimal places past the leading 0s.1). Calculate the Taylor polynomials T2(x) and T3(x) centered at x = a for the given function and value of a. f(x) = ln(x) x , a = 1 please show step by step clearly .