Homework 1, due 18 February 2008

Each problem is worth 10 points.

1. Newton's method for fourth roots is based on the fact that if y is an approximation of the fourth root of x, then a better approximation is the value

x/(y^3) + 3*y
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      4
Use this formula to implement a fourth-root procedure analogous to the square-root procedure.

2. Rewrite the iterative code that appears at the top of page 45 so that the definition of expt-iter is nested inside of the definition of expt using as few variables as possible. (In other words, rewrite this code in the same style that the code for sqrt was rewritten at the bottom of page 30.)