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Problem Summary Let's approximate using what we know about Taylor series. Fact: tan) = 1 - Fact: So, - 4 arctan (1) exactly Fact: The Taylor series for (x) - arctan(x) is P. (*) - Fact: So, x=4 exactly 62n + 1 Let's approximate x by adding up a few terms of this series. Add up 100 terms of this series, and store the result in the variable plApprox You just generated digits of using a Taylor series for tan(x) (evaluated at x = 1 and then multiplied by 4). But even with 100 forms, it wasn't a very good approximation. You need a LOT of terms to get a decent approximation (We say that the series converges slowly- can you think of why?) There are better ways! Here are three other series that could be used: Madhava's representation *=V12 (-3) 1 2+1 Newton's: *=2 24(k! (24+1)! - Ramanujan's: 98017 1 = 2v2 (4k)!(1103 + 26390%) (k!)*3964 For each series, add up to the k= 10 term. Store the corresponding approximations to x in variables called summadhava, sumNewton, and sumRamanujan. Keep in mind that the Ramanujan sum approximates 1/, so it must be inverted at the end to get an approximation to Print the results to the screen, and compare with the actual value of x Use a for loop to fill in an array || 4 solutions submitted (max: 10) | View my solutions Problem Summary One of the most common applications of for loops in MATH 307 is to fill in the entries of an array one at a time. x = [x(1), x(2), x(3),...X(),...x()); I have an array of length 250 named x with random integers from 1 to 10. Create a corresponding array where each onby is computed using the following criteria - If the entry in x is less than 4, define the corresponding entry in y to be 0. . If the entry in x is between 4 and 7 (inclusive), define the corresponding entry iny to be twice the entry inx. - If the entry in x is greater than 7, define the corresponding entry in y to be 100