h(x, y) = cos x coS y. COS x cos
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- Determine the 2nd degree Taylor polynomials Q(x, y) for f(x, y) = ln(x^2 +y^2 + 1) for (x, y) near the point (0, 0).let f(x) = cos(x) and x0 = 0. Find the Taylor polynomial of degree N = 4.Determine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) forf(x, y) = tan−1 (x + 2y) for (x,y) near the point (1,0).
- 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]calculate the Taylor polynomials T2 and T3 centered at x = a for the given function and value of a. f (x) = sin x, a = 0Find T4(x) Taylor polynomial of degree 5 of the function f(x)=cos(x^3) at a=0
- Let 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.Approximate e2 using a 3rd-degree Taylor Polynomial centered at 0, and determine the maximum error of approximation.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.