The square root of 1.5 is obtained by finding the positive root of the quadratic equation 10)-1²-15 If we have two values left and right which define a range known to contain the root, then we can use the bisection method to close in on the actual value. At each step, we calculate the value of fur) at the mid-point of the range and update either left or right depending on which half of the range contains the root Write a function print section stepeix laft, right, ni that prints a table with nat rows, showing the values of left, right, id and fix id) at each iteration. Each value should be printed with 6 digits of accuracy, using a format of 10.61, For example: (left:10.or)(x-right:10.6f) midi10.6f)f(x_mid):16.61)" Notes: You may assume that left and right will always specify a range containing the positive root. • Each table row shows the values before updating the range You should copy the table header from the example below into your code. Hint: You may find the following helper function useful def sign(x) Return the sign of x (a value of either +1 or -1) treating as positive if x < 1 return -11 elsei return 1

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The square root of 1.5 is obtained by finding the positive root of the quadratic equation
fl)-1²-15
If we have two values left and right which define a range known to contain the root, then we can use the bisection method to close in on the actual value. At each step, we calculate the value of for at the mid-point of
the range and update either left or right depending on which half of the range contains the root
Write a function print bisection stepsix left, right, that prints a table with n +1 rows, showing the values of left, right, id and fix aid) at each iteration. Each value should be printed with 6 digits of
accuracy, using a format of 10.6%. For example:
(x_left:18.61Hxright:10.6fHid: 10.6ff(x_mid):10.0f)"
Notes:
• You may assume that left and right will always specify a range containing the positive root.
• Each table row shows the values before updating the range.
•You should copy the table header from the example below into your code.
Hint: You may find the following helper function useful
def sign(x):
Return the sign of x (a value of either +1 or -1) treating e as positive
if x01
return -1
else
return 1
For example
Test
Result
print bisection steps(1, 2, 20)
left right
Rid f(xid)
1.000000 2.000000 1.500000 0.750800
1.000000 1.500000 1.250000 0.002100
1.000000 1.250000 1.125000 -0.234375
1.125000 1.250000 1.187500 -0.009044
1.187500 1.250000 1.218750 -0.014648
1.218750 1.250000 1.234375 0.023682
1.218750 1.234375 1.226562 0.004456
1.218750 1.226562 1.222656 -0.005112)
1.222656 1.226562 1.224409 -0.000332
1.224609 1.226562 1.225586 0.002061
1.224609 1.225586 1.225998 0.000364
1.224409 1.225098 1.224854 0.000266
1.224009 1.224854 1.224731 -0.000033
1.224731 1.224854 1.224792 0.000117
1.224731 1.224792 1.224762 0.000042
1.224731 1.224762 1.224747 0.000004
1.224731 1.224747 1.224739 -0.000014
1.224739 1.224747 1.224743 -0.000005
1.224743 1.224747 1.224745 -0.000000
1.224745 1.224747 1.224746 0.000002
1.224745 1.224746 1.224745 0.000001
Answers (penalty regime: 0, 10, 20 %)
Transcribed Image Text:The square root of 1.5 is obtained by finding the positive root of the quadratic equation fl)-1²-15 If we have two values left and right which define a range known to contain the root, then we can use the bisection method to close in on the actual value. At each step, we calculate the value of for at the mid-point of the range and update either left or right depending on which half of the range contains the root Write a function print bisection stepsix left, right, that prints a table with n +1 rows, showing the values of left, right, id and fix aid) at each iteration. Each value should be printed with 6 digits of accuracy, using a format of 10.6%. For example: (x_left:18.61Hxright:10.6fHid: 10.6ff(x_mid):10.0f)" Notes: • You may assume that left and right will always specify a range containing the positive root. • Each table row shows the values before updating the range. •You should copy the table header from the example below into your code. Hint: You may find the following helper function useful def sign(x): Return the sign of x (a value of either +1 or -1) treating e as positive if x01 return -1 else return 1 For example Test Result print bisection steps(1, 2, 20) left right Rid f(xid) 1.000000 2.000000 1.500000 0.750800 1.000000 1.500000 1.250000 0.002100 1.000000 1.250000 1.125000 -0.234375 1.125000 1.250000 1.187500 -0.009044 1.187500 1.250000 1.218750 -0.014648 1.218750 1.250000 1.234375 0.023682 1.218750 1.234375 1.226562 0.004456 1.218750 1.226562 1.222656 -0.005112) 1.222656 1.226562 1.224409 -0.000332 1.224609 1.226562 1.225586 0.002061 1.224609 1.225586 1.225998 0.000364 1.224409 1.225098 1.224854 0.000266 1.224009 1.224854 1.224731 -0.000033 1.224731 1.224854 1.224792 0.000117 1.224731 1.224792 1.224762 0.000042 1.224731 1.224762 1.224747 0.000004 1.224731 1.224747 1.224739 -0.000014 1.224739 1.224747 1.224743 -0.000005 1.224743 1.224747 1.224745 -0.000000 1.224745 1.224747 1.224746 0.000002 1.224745 1.224746 1.224745 0.000001 Answers (penalty regime: 0, 10, 20 %)
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