(a) If x is a floating-point number close to 1, then the evaluation of g(x) V - 1 - 1 in floating-point arithmetic may be very inaccurate due to subtractive cancellation. Illustrate this using base b = 10, precision k = 4, idealized, chopping floating-point arithmetic with x = 1.004 to show that f(g(1.004)) is not an accurate approximation of g(1.004). 2 (b) Determine the third order (n = 3) Taylor series approximation for f(x) = Vv, ex- panded about a = 1. Show all your work and do not expand any terms involving (x - 1). (C) Substitute the above Taylor polynomial approximation in (b) into the formula for g(x), and simplify in order to obtain a good polynomial approximation for g(x). Do not expand any terms involving (x 1). (d) Show that your polynomial approximation to g(x) obtained in part (c) gives a more accurate numerical approximation to g(1.004) when using b = 10, precision k = 4, idealized, chopping floating-point arithmetic