USB 3.1 offers an improvement over its predecessors by enabling a maximum data transfer rate of up to:

1. package newton’s method for approximating square roots (case study 3.6) in a function named newton. this function expects the input number as an argument and returns the estimate of its square root. the script should also include a main function that allows the user to compute square roots of inputs until she presses the enter/return key. 2. convert newton’s method for approximating square roots in project 1 to a recursive function named newton. (hint: the estimate of the square root should be passed as a second argument to the function.) 3. elena complains that the recursive newton function in project 2 includes an extra argument for the estimate. the function’s users should not have to provide this value, which is always the same, when they call this function. modify the definition of the function so that it uses a keyword parameter with the appropriate default value for this argument, and call the function without a second argument to demonstrate that it solves this problem. 4. restructure newton’s method (case study 3.6) by decomposing it into three cooperating functions. the newton function can use either the recursive strategy of project 1 or the iterative strategy of case study 3.6. the task of testing for the limit is assigned to a function named limitreached, whereas the task of computing a new approximation is assigned to a function named improveestimate. each function expects the relevant arguments and returns an appropriate value. 5. a list is sorted in ascending order if it is empty or each item except the last one is less than or equal to its successor. define a predicate issorted that expects a list as an argument and returns true if the list is sorted, or returns false otherwise. (hint: for a list of length 2 or greater, loop through the list and compare pairs of items, from left to right, and return false if the first item in a pair is greater.)

Least square fit to polynomial write a function leastsquarefit3pol that solves a linear system of equations to find a least squares fit of a third order polynomial to an experimental data set given as two row arrays. the function leastsquarefit3pol must explicitly solve a set of linear equations and cannot use polyfit. there should be no restriction on the size of the problem that can be solved.

Write a program that uses a random number generator to generate a two digit positive integer and allows the user to perform one or more of the following operations: a. double the number. b. reverse the digits of the number. c. raise the number to the power of 2, 3, or 4. d. sum the digits of the number. e. if the number is a two-digit number, then raise the first digit to the power of the second digit. f. if the number is a three-digit number and the last digit is less than or equal to 4, then raise the first two digits to the power of the last digit. after performing an operation if the number is less than 10, add 10 to the number. also, after each operation determine if the number is prime. each successive operation should be performed on the number generated by the last operation. your program should not contain any global variables and each of these operations must be implemented by a separate function. also, your program should be menu driven. 7. (fraction calculator) write a program that