Radical roots - Solution
Enter the function y(t)=t^2-2049
Tap on y(t) in the menu and then on the submenu (⋮) and select 'General'Enter the function as above and click OK.
Change the View settings so that the derivative is not shown
Select the View Icon and from the View window slide off the Derivative toggle.
Change the t-axis
Tap on the settings icon and then the submenu (...) and select 't-axis' and change the range to 40 to 50 and tap on OK.
y(t)=t^2-2049 with 40<=t<50
Tap on the 'Mode' icon and then on the submenu (...) and select 'Zero Find'. Change the Accuracy (No. of s.f.) to 14 and the number of iterations to 100. Now enable 'User-defined' and tap on 'FUNCTION' next to this toggle switch.
On the define function window which appears enter
y(t)=40+449/(40+t) and then tap OK.
The fix point function will now be displayed under the User-defined heading.
Tap on OK from this Zero-find window.
You will get the message popup "Click on the t-axis" and after tapping OK on this popup then click once on the t-axis in the vicinity of where the graph crosses the t-axis. After performing the zero-finding plotXpose will display the result and the sequence of values found during the calculation. An example output is below, where the user defined fix point method has calculated the square root of 2049 as 45.265881191025 to 14 significant figures.
Solving t^2-2049=0: Success. The Fix point method, using function 40+449/(40+t) has converged to the value (45.265881191025,0.00000000000000E+000).
The sequence of values found was
( n, t , y(t))
(0, 46.7320251464844, 1.348821742916480E+002)
(1, 45.1768651687963, -8.050853520399187E+000)
(2, 45.271384420056, 4.982473084855883E-001)
(3, 45.2655413425467, -3.076696619245922E-002)
(4, 45.2659021795942, 1.900132594983006E-003)
(5, 45.2658798948058, -1.173490195469640E-004)
(6, 45.2658812710775, 7.247283974720631E-006)
(7, 45.2658811860812, -4.475805326364934E-007)
(8, 45.2658811913304, 2.764181772363372E-008)
(9, 45.2658811910062, -1.707121555227786E-009)
(10, 45.2658811910263, 1.055013854056597E-010)
(11, 45.265881191025, -6.366462912410498E-012)
(12, 45.2658811910251, 0.000000000000000E+000)
(13, 45.2658811910251, 0.000000000000000E+000)
The sequence of values found was
( n, t , y(t))
(0, 46.7320251464844, 1.348821742916480E+002)
(1, 45.1768651687963, -8.050853520399187E+000)
(2, 45.271384420056, 4.982473084855883E-001)
(3, 45.2655413425467, -3.076696619245922E-002)
(4, 45.2659021795942, 1.900132594983006E-003)
(5, 45.2658798948058, -1.173490195469640E-004)
(6, 45.2658812710775, 7.247283974720631E-006)
(7, 45.2658811860812, -4.475805326364934E-007)
(8, 45.2658811913304, 2.764181772363372E-008)
(9, 45.2658811910062, -1.707121555227786E-009)
(10, 45.2658811910263, 1.055013854056597E-010)
(11, 45.265881191025, -6.366462912410498E-012)
(12, 45.2658811910251, 0.000000000000000E+000)
(13, 45.2658811910251, 0.000000000000000E+000)
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plotXpose app is a companion to the book Mathematics for Electrical Engineering and Computing by Mary Attenborough, published by Newnes, 2003.