Due Date: Monday, October 30, during class

Use this link to submit your team result by the Use the Lab 8 menu choice and "Code" as the type

__Educational goals of this lab - verify that every student can__

- import a function from the math library
- use a loop for an iterative process
- write a function definition
- call a function properly
- understand arguments and parameters
- understand using a debugger
- work together with their team to solve a larger problem
- Newton's method starts with an initial guess for the square root of
a number
*n*of*n*/ 2. The following guess is calculated asnewguess = 0.5 * (oldguess + n/oldguess)

Note that oldguess needs to be updated repeatedly to get the next value of newguess. **(34 points)**Write a function called**newton**- The function has two parameters: the number to have its square root found, and the number of iterations.
- The function should output to the screen the approximations as they are calculated.
- The function should return the final value of the process.
- The function should have a standard header with the 3 P's.
**(26 points)**Write a main function to be the driver for the newton function, It will ask for a number to find the square root of and the number of iterations desired. The first number should be a float, the second an integer. The driver should show the difference between the result of newton and the math library sqrt function result.- Note the driver handles a negative number to find the square root of by taking the absolute value of the input.
- The main function should have a header comment as well.
- Sample run
Enter the number you want the square root of: 25 The number of iterations? 10 Iteration 1 approximation 12.5 Iteration 2 approximation 7.25 Iteration 3 approximation 5.349137931034482 Iteration 4 approximation 5.011394106532552 Iteration 5 approximation 5.000012953048684 Iteration 6 approximation 5.000000000016778 Iteration 7 approximation 5.0 Iteration 8 approximation 5.0 Iteration 9 approximation 5.0 Iteration 10 approximation 5.0 sqrt of 25.0 from math library function 5.0 Difference 0.0

Another run

Enter the number you want the square root of: 27 The number of iterations? 5 Iteration 1 approximation 13.5 Iteration 2 approximation 7.75 Iteration 3 approximation 5.616935483870968 Iteration 4 approximation 5.211913542366209 Iteration 5 approximation 5.196176253962744 sqrt of 27.0 from math library function 5.196152422706632 Difference 2.383125611160608e-05

Run with a negative number input

Enter the number you want the square root of: -8 The number of iterations? 10 Iteration 1 approximation 4.0 Iteration 2 approximation 3.0 Iteration 3 approximation 2.833333333333333 Iteration 4 approximation 2.8284313725490193 Iteration 5 approximation 2.8284271247493797 Iteration 6 approximation 2.82842712474619 Iteration 7 approximation 2.82842712474619 Iteration 8 approximation 2.82842712474619 Iteration 9 approximation 2.82842712474619 Iteration 10 approximation 2.82842712474619 sqrt of 8.0 from math library function 2.8284271247461903 Difference -4.440892098500626e-16

**(10 points)**Test cases- Write 6 test cases for this program. Include them in a comment at the bottom of the program.
- Three of them should test the number of iterations in loop in the newton function.
- Three of them should test the number to take the square root of.
- Give the usual components of a test case (description, inputs, expected output) on one line with commas between.

- Write 6 test cases for this program. Include them in a comment at the bottom of the program.
- Submit your finished program with the link at the top of the page. Use the Lab 8 and Code menu choices.
**(10 points)**Use the debugger (either IDLE's or WingIDE's)- Use a debugger to set a breakpoint at the newton function call in the main.
- Show your TA that you can step into the newton function definition.
- Step through one iteration of your newton function's loop.

Log off properly - you don't want your account misused by someone else!

Remember NOT to leave files on the

**local**hard drives in this lab or anywhere else on campus! Make sure you save your projects onto a portable storage device you take with you!

__INSTRUCTIONS:__

Please read this tutorial on Debugging with IDLE.

**(60 points) Team Problem:** Newton's method for square root