a) Use the Taylor theorem for the function U(x, t) = te*t with the step size Ax (t, is held constant) b) Use the Taylor theorem for the function U(x, t) = text with the step size At (x, is held constant). %3D
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- find the Taylor polynomial at x = a for the given function. f (x) = x ln(x), T4, a = 1In the study of a nonlinear spring with periodic forcing, the equation y''+ky+ry3= Acos(ωt) arises. Let k = 4, r = 8, A = 1, and ω = 6. Find the first three nonzero terms in the Taylor polynomial approximation to the solution with initial values y(0) = 0, y'(0)=1. The Taylor approximation to three nonzero terms is y(t) =?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]
- What is the 1st-order Taylor polynomial of: f(x,y) = e(x+y) -1 at (0,0)Determine the first three nonzero terms in the Taylor polynomial approximation for the given initial value problem. 4x'' + 3tx=0; x(0)=1, x'(0)=0 The Taylor approximation to three nonzero terms is x(t)=?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.