Suppose we have a computer that can't divide. One way to get around this is to...

 

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Suppose we have a computer that can't divide. One way to get around this is to create a routine that finds the roots of f(x) = - a. We then input a and get its inverse. (You (human) can use division in formulating the algorithm, but the algorithm must not require the computer to divide.) Show how you would use Newton-Raphson to do this. Show if/when it converges. What is the order of the convergence? Suppose we have a computer that can't divide. One way to get around this is to create a routine that finds the roots of f(x) = - a. We then input a and get its inverse. (You (human) can use division in formulating the algorithm, but the algorithm must not require the computer to divide.) Show how you would use Newton-Raphson to do this. Show if/when it converges. What is the order of the convergence?