Question

Part 1

Encapsulate the following Python code from Section 7.5 in a function named my_sqrt that takes a as a parameter, chooses a starting value for x, and returns an estimate of the square root of a.

while True:
y = (x + a/x) / 2.0
if y == x:
break
x = y

Part 2

Write a function named test_sqrt that prints a table like the following using a while loop, where "diff" is the absolute value of the difference between my_sqrt(a) and math.sqrt(a).

a = 1 | my_sqrt(a) = 1 | math.sqrt(a) = 1.0 | diff = 0.0
a = 2 | my_sqrt(a) = 1.41421356237 | math.sqrt(a) = 1.41421356237 | diff = 2.22044604925e-16
a = 3 | my_sqrt(a) = 1.73205080757 | math.sqrt(a) = 1.73205080757 | diff = 0.0
a = 4 | my_sqrt(a) = 2.0 | math.sqrt(a) = 2.0 | diff = 0.0
a = 5 | my_sqrt(a) = 2.2360679775 | math.sqrt(a) = 2.2360679775 | diff = 0.0
a = 6 | my_sqrt(a) = 2.44948974278 | math.sqrt(a) = 2.44948974278 | diff = 0.0
a = 7 | my_sqrt(a) = 2.64575131106 | math.sqrt(a) = 2.64575131106 | diff = 0.0
a = 8 | my_sqrt(a) = 2.82842712475 | math.sqrt(a) = 2.82842712475 | diff = 4.4408920985e-16
a = 9 | my_sqrt(a) = 3.0 | math.sqrt(a) = 3.0 | diff = 0.0

Modify your program so that it outputs lines for a values from 1 to 25 instead of just 1 to 9.

You should submit a script file and a plain text output file (.txt) that contains the test output. Multiple file uploads are permitted.

Your submission will be assessed using the following Aspects.

1. Does the submission include a my_sqrt function that takes a single argument and includes the while loop from the instructions?
2. Does the my_sqrt function initialize x and return its final value?
3. Does the test_sqrt function print a values from 1 to 25?
4. Does the test_sqrt function print the values returned by my_sqrt for each value of a?
5. Does the test_sqrt function print correct values from math.sqrt for each value of a?
6. Does the test_sqrt function print the absolute value of the differences between my_sqrt and math.sqrt for each value of a?
7. Does the my_sqrt function compute values that are almost identical to math.sqrt ("diff" less than 1e-14)?

Answer 1

import math

def my_sqrt(a):

x = 1

while True:

    y = (x + a/x) / 2.0

    if y == x:

      break

    x = y

return y

for a in range(1,10):

print("a = ",a, "| my_sqrt(a) = ",my_sqrt(a),"| math.sqrt(a) = ",math.sqrt(a), "| diff = ",abs(my_sqrt(a)-math.sqrt(a)))

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SEE OUTPUT/IMAGE FOR INDENTATION

PLEASE COMMENT if there is any concern.

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