programming in python

Assignment 1-programming in python Q1) Newton's algorithm for finding the square root of N: (101 Ch 8) 1.Start with the initial approximation 1. 2.As long as the approximation isn't close enough, repeatedly: a.Refine the approximation using the formula newapp=loldapp+poldapp)/2 While reading Newton's algorithm, you might have noticed that the stopping condition is what vague. Since some numbers' square roots (such as the square root of 2) cannot be represented as finite fractions, Newton's algorithm will not always be able to find the exact square root. However, each successive approximation is guaranteed to be closer to the square root. Thus, the person using the algorithm can determine exactly how close the approximation needs to be in order to suffice. For example, zuppose that we wanted to find the square root of 1024. Newton's algorithm starts with the initial approximation 1. The next approximation is obtained by plugging 1 into Newton's formula; we therefore evaluate the expression (1 + 1024/1)/2, which yield: 512.5. The next approximation is (512.5 +1024/512.5)/2 = 257.2, followed by (257.2-1024/257.2)2 = 130.6, and 30 on. After only- 10 refinements, the approximation is so close to the actual square root, 32, that a computer will round the value to 32 (see the figure). Initial approximation - 1 Next approximation - 512.5 Next approximation - 257.2490243902 439 Next approximation = 130.61480157022683 Next approximation 69.2 2732405448894 Yext approximation 42.00958563 100627 Next approximation = 33. 19248741685438 Next approximation 32.02142090500024 Next approximation 32.0000071648159 Next approximation 32.0000000000008 Next approximation - 32 Q2) Find the dimensions, rand h, for a cylinder that has 1,000 square centimeters of material and maximum volume. What is the maximum volume that is achieved: Give all answers accurate to three decimal places