show detailed working The Taylor polynomial of degree n about x = a for the func

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The Taylor polynomial of degree n about x = a for the function f is given by with error f(x) - pn(x) = f(n+1)(Cx)(x-a)n+1/(n+1)! where cx is between a and x. Let f(x)=x1/3 for x R For this f, find P2(x) about x = 1. Show that an approximation to 10901/3 is given by 10p2(1.09). Then calculate 10p2(1.09). For the approximation to 10901//3 obtained in part (b), obtain an upper bound on the absolute error. Verify that the true absolute error is less than this upper bound. Suppose we want to calculate the function for values of x close to zero. Why would we not expect the values calculated using this expression for g(x) to be very accurate? Use the approximation and a corresponding one for e-x to obtain an expression for an approximation to the g given in part (d) which is expected to be more accurate for values of x close to zero.

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