# Converging sequence - Solution

Plot of

## y(t)=2*t^3-12*t^2+14*t+5

We have used the view menu to switch off the derivative display and display a grid, and used the Settings menu to change the t-axis limits to -1 to 5

## Numerically solve 2*t^3-12*t^2+14*t+5 =0 using the Bisection method

Tap on the Mode icon and then the submenu ⋮ and select Zero Find. Change the radio to 'Bisection Method' the 'No. of s.f.' to 14 and the No. of iterations to 100. Example result below.

Solving 2*t^3-12*t^2+14*t+5=0: Success. The Bisection method has converged to the value (2.1002012096889,1.06581410364015E-014).
The sequence of values found was
( n, t , y(t))
(0, 1.26143789291382, 7.579888237905269E+000)
(1, 3.08496737480164, -7.295325934282026E+000)
(2, 2.17320263385773, -7.216344741674874E-001)
(3, 1.71732026338577, 3.781620715492245E+000)
(4, 1.94526144862175, 1.547057486553449E+000)
(5, 2.05923204123974, 4.080952111014113E-001)
(6, 2.11621733754873, -1.590340036264806E-001)
(7, 2.08772468939424, 1.241032980041723E-001)
(8, 2.10197101347148, -1.758952765572985E-002)
(9, 2.09484785143286, 5.322801001449307E-002)
(10, 2.09840943245217, 1.781175132050805E-002)
(11, 2.10019022296183, 1.092054840512446E-004)
(12, 2.10108061821666, -8.740641908374869E-003)
(13, 2.10063542058924, -4.315837888363205E-003)
(14, 2.10041282177554, -2.103346055015720E-003)
(15, 2.10030152236868, -9.970777404220144E-004)
(16, 2.10024587266525, -4.439379908802721E-004)
(17, 2.10021804781354, -1.673667189550088E-004)
(18, 2.10020413538768, -2.908073382457133E-005)
(19, 2.10019717917476, 4.006234601661163E-005)
(20, 2.10020065728122, 5.490798827167964E-006)
(21, 2.10020239633445, -1.179496931058566E-005)
(22, 2.10020152680784, -3.152085696456197E-006)
(23, 2.10020109204453, 1.169356451669046E-006)
(24, 2.10020130942618, -9.913646437098578E-007)
(25, 2.10020120073536, 8.899588976873929E-008)
(26, 2.10020125508077, -4.511843769705592E-007)
(27, 2.10020122790806, -1.810942436009100E-007)
(28, 2.10020121432171, -4.604916981065799E-008)
(29, 2.10020120752853, 2.147336175539749E-008)
(30, 2.10020121092512, -1.228790580398709E-008)
(31, 2.10020120922683, 4.592731528418881E-009)
(32, 2.10020121007597, -3.847588914140943E-009)
(33, 2.1002012096514, 3.725695307821297E-010)
(34, 2.10020120986369, -1.737511468036246E-009)
(35, 2.10020120975754, -6.824620868428610E-010)
(36, 2.10020120970447, -1.549551598145627E-010)
(37, 2.10020120967794, 1.088089618406229E-010)
(38, 2.1002012096912, -2.307132263013045E-011)
(39, 2.10020120968457, 4.287414867576445E-011)
(40, 2.10020120968789, 9.901413022816996E-012)
(41, 2.10020120968955, -6.586731160496129E-012)
(42, 2.10020120968872, 1.655564574321033E-012)
(43, 2.10020120968913, -2.454925152051146E-012)
(44, 2.10020120968892, -3.907985046680551E-013)
(45, 2.10020120968882, 6.252776074688882E-013)
(46, 2.10020120968887, 1.172395514004165E-013)
(47, 2.1002012096889, -1.421085471520200E-013)
(48, 2.10020120968888, -1.421085471520200E-014)
(49, 2.10020120968888, 5.329070518200751E-014)
(50, 2.10020120968888, 1.065814103640150E-014)

Tap on the File menu and then tap 'Save Zero Find Sequence'. Tap Open and read in the values as a new function. See result below.

From the plot of the zero-find sequence we can see that the values initially oscillate and then gradually approach the value of 2.1002012096889 which is a zero of 2*t^3-12*t^2+14*t+5 expressed to 14 s.f.

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