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Use Regula False Method to Find the Real Root of the Equation

by Ansar
(Paksitan)












































use regula false method to find the real root of the equation


x^3-sinx +1=0

correct to four decimal places after three succesive approximation is (-2,-1)


Note : all the calculation should be done in radian mode only.

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Oct 20, 2011
Regula Falsi Method to Find the Real Root of the Equation
by: Staff

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Part II


-60 . . . . . . .-1.0472 . . . . . . . .-1.14838 . . . . . . .-0.86602 . . . . . . .0.717647
-61 . . . . . . .-1.06465 . . . . . . .-1.20676 . . . . . . .-0.87462 . . . . . . .0.66786
-62 . . . . . . .-1.0821 . . . . . . . .-1.26709 . . . . . . .-0.88295 . . . . . . .0.615861
-63 . . . . . . .-1.09956 . . . . . . .-1.32939 . . . . . . .-0.89101 . . . . . . .0.561615
-64 . . . . . . .-1.11701 . . . . . . .-1.39371 . . . . . . .-0.89879 . . . . . . .0.505088
-65 . . . . . . .-1.13446 . . . . . . .-1.46006 . . . . . . .-0.90631 . . . . . . .0.446246
-66 . . . . . . .-1.15192 . . . . . . .-1.52849 . . . . . . .-0.91355 . . . . . . .0.385054
-67 . . . . . . .-1.16937 . . . . . . .-1.59903 . . . . . . .-0.9205 . . . . . . . .0.321479
-68 . . . . . . .-1.18682 . . . . . . .-1.6717 . . . . . . . .-0.92718 . . . . . . .0.255486
-69 . . . . . . .-1.20428 . . . . . . .-1.74654 . . . . . . .-0.93358 . . . . . . .0.187041
-70 . . . . . . .-1.22173 . . . . . . .-1.82358 . . . . . . .-0.93969 . . . . . . .0.116111
-71 . . . . . . .-1.23918 . . . . . . .-1.90286 . . . . . . .-0.94552 . . . . . . .0.042662
-72 . . . . . . .-1.25664 . . . . . . .-1.9844 . . . . . . . .-0.95106 . . . . . . .-0.03334
-73 . . . . . . .-1.27409 . . . . . . .-2.06823 . . . . . . .-0.9563 . . . . . . . .-0.11193
-74 . . . . . . .-1.29154 . . . . . . .-2.1544 . . . . . . . .-0.96126 . . . . . . .-0.19314
-75 . . . . . . .-1.309 . . . . . . . . .-2.24293 . . . . . . .-0.96593 . . . . . . .-0.277
-76 . . . . . . .-1.32645 . . . . . . .-2.33384 . . . . . . .-0.9703 . . . . . . . .-0.36355
-77 . . . . . . .-1.3439 . . . . . . . .-2.42719 . . . . . . .-0.97437 . . . . . . .-0.45282
-78 . . . . . . .-1.36136 . . . . . . .-2.52299 . . . . . . .-0.97815 . . . . . . .-0.54484
-79 . . . . . . .-1.37881 . . . . . . .-2.62127 . . . . . . .-0.98163 . . . . . . .-0.63965
-80 . . . . . . .-1.39626 . . . . . . .-2.72208 . . . . . . .-0.98481 . . . . . . .-0.73727
-81 . . . . . . .-1.41372 . . . . . . .-2.82544 . . . . . . .-0.98769 . . . . . . .-0.83775
-82 . . . . . . .-1.43117 . . . . . . .-2.93138 . . . . . . .-0.99027 . . . . . . .-0.94112


As you can see, the solution to the equation x³ - sin(x) +1 = 0 occurs when x ≈ -1.24 radians (about -71.5 degrees)

you can see a graph of this function by opening the link shown below

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http://www.solving-math-problems.com/images/graph-function-2011-10-19.png


Thanks for writing.

Staff
www.solving-math-problems.com


Oct 20, 2011
Regula Falsi Method to Find the Real Root of the Equation
by: Staff


Part I

Question:

by Ansar
(Pakistan)

use regula false method to find the real root of the equation


x^3-sinx +1=0

correct to four decimal places after three successive approximation is (-2,-1)


Note : all the calculation should be done in radian mode only.


Answer:

The Regula Falsi method is a trial and error method of solving equations.

It is also called the “guess and check” method. Test values are substituted for variables in an equation to see which values work.

x³ - sinx +1 = 0


You can use excel to generate as many calculations as you need. These are some of the figures I used:

column 1: x in degrees

column 2: x in radians = x*3.14159/180

column 3: x^3 using x in radians

column 4: sin(x) using x in radians

column 5: x^3 – sin(x) +1 , using x in radians

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