Let a be a constant. State the formula for the nth-degree Taylor polynomial of a continuous function g(t) at a. As well, find the third degree Taylor Polynomial of f(r) = VT+x at 0, and use it to approximate the value of V.
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- Determine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) forf(x, y) = x √y for (x,y) near the point (1,4).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]Approximate e2 using a 3rd-degree Taylor Polynomial centered at 0, and determine the maximum error of approximation.
- If y'=x3+y2, where y=1 when x=0, find a degree 3 polynomial that best fits the solution using Taylor Series Polynomial.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).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.
- Find first 3 terms of the Taylor expansion of the function f(x,y) = e ^ (x+y) at the point (0,0).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.Calculate the third degree Taylor polynomial of f (x) = e2x + cosx centered at x = 0.