Let a number * be an approximation of a number az and the corresponding relative error is equal to n > 0. One of the standard, and widely used, ways to measure accuracy of the approximation is to find the corresponding number of significant digits. By the definition, the approximation r has k significant digits if k is the maximal natural number such that RE(za*)= n < 4. (Floating-Point Arithmetic; Taylor Polynomials). It is known that = 4. (arctan (33/74) - arctan(-41/107)). 10% Next, the Taylor (Maclaurin) polynomial of degree nine for the arctangent function about zero is 25 27 5 T(x)=x- + (i) Find an approximation y* of as y =4-(T(33/74) - T(-41/107)), as suggested by the above reasoning. All calculations are to be carried out in the 7-digit floating-point arithmetic (FPA). To evaluate the representation T(33/74) in the FPA, the with a scientific calculator, perform the following steps: (1) switch to (Sci 7) mode, (2) type and execute the following commands one by one: 3374 X X - x^33 + x^55 - x^77+X^99 A After the above program is executed, the required value will be stored in the variable A. Work similarly, to find the representation of T(-41/107) in the FPA7, but, this time, store the resulting value in the variable B. Finish the calculations by executing the command 4 x (A B) Y. (ii) Use the 12-digit representation y = 3.14159265359 of a to find the relative error and the number of significant digits in the approximation yy of y by y.