1. The measurement, x, is an unbiased estimate of μ and has precision o. Expand x2 in a Taylor series about the point x = μ. Hence show that, if the coefficient of variation of x is small, the expected value of z = x² is given by u²+o² and that the coefficient of variation of z is approximately twice as large as that of x.
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- Find Taylor series at x = 0 for the functions e(πx/2)Linearize the next non-linear function using the Taylor series in the region 2 ≤ x ≤ 4 and 1 ≤ y ≤ 5. Find the error if the linearized equation is used to calculate the function when x = 2.5 and y = 4.25.y' = 1+xy2 and y(0)=2, find the power series solution up to 10 consecutive terms by using the Taylor series method.
- for the f(x)=e^x function ; find the a=3 centered taylor series and approximation radius.decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem .If false,provide an example,illustration,or brief explanation of why the statement is false.Q.)`The coefficients a0 and a1 in the power series solution to an initial-value problem y′′+p(x)y′+q(x)y =0, where p(x) and q(x) are analytic at x = x0, are the values y(x0) and y′(x0), respectively