(c) Solve the following equation correct to 5 significant figures using Regula-Falsi Method.x3 +x2 +3x−4 = 0The root must be in the interval [0,1].(d) Solve the following equation correct to 5 significant figures using Bisection Method.x sin(2x) +e2x +3x−3 = 0The root must be in the interval [0,0.5].(e) [ The Method of Iteration ] Perform seven iterations to find a real root of the equationsy2 −5y+4 = 03yx2 −10x+7 = 0using the iteration method.(f) [ The Method of Iteration ] Perform seven iterations to find a real root of the equationsy2 −5y+4 = 03yx2 −10x+7 = 0using the iteration meth PROBLEM ONE(a) Solve the following equation correct to 5 significant figures using Newton's Method.4x – sin(x?) +e-2t } -x²+2 =0Take the initial guess as xo = 1.75.(b) Solve the following equation correct to 5 significant figures using Secant Method.2x - x² – x – 7 = 0The root must be in the interval [1,1.3].Mathematics can smile!2.(c) Solve the following equation correct to 5 significant figures using Regula-Falsi Method.x³+x² + 3x – 4 = 0The root must be in the interval [0, 1].(d) Solve the following equation correct to 5 significant figures using Bisection Method.x sin(2x) +e2* + 3x – 3 = 0The root must be in the interval [0,0.5].(e) [ The Method of Iteration] Perform seven iterations to find a real root of the equationsy? – 5y +4 = 03yx – 10x +7 = 0using the iteration method.(f) [ The Method of Iteration] Perform seven iterations to find a real root of the equationsy – 5y +4 =0Зух?- 10х +7 3 0using the iteration method.(g) [ The Newton-Raphson Method | Perform two iterations to find a real root of the equationsy? – 5y +4 = 03yx? – 10x+7 = 0using the Newton-Rhaphson method and let xo = yo = 0.5.(h) [ The Newton-Raphson Method | Perform two iterations to find a real root of the equationssinx -y= -0.9793cos y -x = -0.6703using the Newton-Raphson method and let xo = 0.5, yo = 1.5.(i) Find a recurrence formula for solving V6 and hence approximate its value correct to 5significant figure.(j) Solve the following equation correct to 5 significant figures using Newton's Method.4x +x? – x – 3 = 0Take the initial guess as xo = 0.85.Mathematics can smile!PROBLEM TWO(a) Using Newton's forward difference formula, find the sumS, = 1+2 + 33 +4³ + ... +n°.(b) Values of x (in degrees) ans sinx are given in the following table.x (in degrees)sinx150.25881900.34202010.42261832025300.5350.5735764

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(c) Solve the following equation correct to 5 significant figures using Regula-Falsi Method.
x
3 +x
2 +3x−4 = 0
The root must be in the interval [0,1].
(d) Solve the following equation correct to 5 significant figures using Bisection Method.
x sin(2x) +e
2x +3x−3 = 0
The root must be in the interval [0,0.5].
(e) [ The Method of Iteration ] Perform seven iterations to find a real root of the equations
y
2 −5y+4 = 0
3yx2 −10x+7 = 0
using the iteration method.
(f) [ The Method of Iteration ] Perform seven iterations to find a real root of the equations
y
2 −5y+4 = 0
3yx2 −10x+7 = 0
using the iteration meth

PROBLEM ONE
(a) Solve the following equation correct to 5 significant figures using Newton's Method.
4x – sin(x?) +e-2t } -x²+2 =0
Take the initial guess as xo = 1.75.
(b) Solve the following equation correct to 5 significant figures using Secant Method.
2x - x² – x – 7 = 0
The root must be in the interval [1,1.3].
Mathematics can smile!
2.
(c) Solve the following equation correct to 5 significant figures using Regula-Falsi Method.
x³+x² + 3x – 4 = 0
The root must be in the interval [0, 1].
(d) Solve the following equation correct to 5 significant figures using Bisection Method.
x sin(2x) +e2* + 3x – 3 = 0
The root must be in the interval [0,0.5].
(e) [ The Method of Iteration] Perform seven iterations to find a real root of the equations
y? – 5y +4 = 0
3yx – 10x +7 = 0
using the iteration method.
(f) [ The Method of Iteration] Perform seven iterations to find a real root of the equations
y – 5y +4 =0
Зух?- 10х +7 3 0
using the iteration method.
(g) [ The Newton-Raphson Method | Perform two iterations to find a real root of the equations
y? – 5y +4 = 0
3yx? – 10x+7 = 0
using the Newton-Rhaphson method and let xo = yo = 0.5.
(h) [ The Newton-Raphson Method | Perform two iterations to find a real root of the equations
sinx -y= -0.9793
cos y -x = -0.6703
using the Newton-Raphson method and let xo = 0.5, yo = 1.5.
(i) Find a recurrence formula for solving V6 and hence approximate its value correct to 5
significant figure.
(j) Solve the following equation correct to 5 significant figures using Newton's Method.
4x +x? – x – 3 = 0
Take the initial guess as xo = 0.85.
Mathematics can smile!
PROBLEM TWO
(a) Using Newton's forward difference formula, find the sum
S, = 1+2 + 33 +4³ + ... +n°.
(b) Values of x (in degrees) ans sinx are given in the following table.
x (in degrees)
sinx
15
0.2588190
0.3420201
0.4226183
20
25
30
0.5
35
0.5735764

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