Assignment: Python Functions
Part I
Encapsulate the following Python code 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 II
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 that contains the test output. Multiple file uploads are permitted.
Your submission will be assessed using the following Aspects.
o Does the submission include a my_sqrt function that takes a single argument and includes the while loop from the instructions?
o Does the my_sqrt function initialize x and return its final value?
o Does the test_sqrt function print a values from 1 to 25?
o Does the test_sqrt function print the values returned by my_sqrt for each value of a?
o Does the test_sqrt function print correct values from math.sqrt for each value of a?
o Does the test_sqrt function print the absolute value of the differences between my_sqrt and math.sqrt for each value of a?
o Does the my_sqrt function compute values that are almost identical to math.sqrt ("diff" less than 1e-14)?
Format your assignment according to the following formatting requirements:
o The answer should be typed, using Times New Roman font (size 12), double spaced, with one-inch margins on all sides.
o The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
o Also include a reference page. The Citations and references must follow APA format. The reference page is not included in the required page length.