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Homework answers / question archive / Name the problem as HW1Problem2
Name the problem as HW1Problem2.m Write a script to do the following items. 1) Find Taylor expansion of f(x) = arctan (x), i.e., Pn (x), for n = 1, 2, .... Here is the commend in MATLAB f= atan(x); P(n) = taylor(f, x, 'Order', n); 2) Now, we want to use this Taylor approximations to find the value of pi, (TI), for a given accuracy. Suppose, this can be done by following recursive formulas 4[Pn () + Pn] (1) and 16P, () – 4Pm670) (2) on which, for example, Pn (1) means nth Taylor approximation of f(x) = arctan (x) evaluated at x = 12 / 3) Use these two formulas to approximate n for the accuracy of 20-digit. In another word, find n on which the error is 10-21 for each separate above formula (1) and (2). i.e., E = abs((11 – approx1 or 2)) < 10-21, where n = pi is MATLAB calculation of it and approx) is approximation of it by (1) and approx2 is approximation of it by (2). 4) Write down in a commend line (in the end of your script) that which formula (1) or (2) is more accurate in calculating n.
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