EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 5, Problem 12P
Given
Use bisection to determine the maximum of this function. Employ initial guesses of
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2. Answer the question completely and write down the given, required and formula that had been used. Provide graph and accurate/comple solution.
The value are:
V- 1
X- 5
W- 7
Y- 6
Z- 8
A root of the function
f(x) = x3 – 10x² +5
lies close to x = 0.7. Doing three iterations, compute this root using the Newton-
Raphson method with an initial guess of x=1).
Newton-Raphson iterative equation is given as:
f(x;)
Xi+1 = Xị -
f'(xi)
Find the three unknown on this problems using
Elimination Method and Cramer's Rule. Attach your
solutions and indicate your final answer.
Problem 1.
7z 5y
3z
16
%3D
3z
5y + 2z
-8
%3D
5z + 3y
7z
= 0
Problem 2.
4x-2y+3z 1
*+3y-4z -7
3x+ y+2z 5
Chapter 5 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 5 - 5.1 Determine the real roots...Ch. 5 - 5.2 Determine the real root of:
(a) Graphically....Ch. 5 - 5.3 Determine the real root of:
(a)...Ch. 5 - Determine the roots of f(x)=1221x+18x22.75x3...Ch. 5 - Locate the first nontrivial root of sin x=x2wherex...Ch. 5 - 5.6 Determine the positive real root of (a)...Ch. 5 - 5.7 Determine the real root of:...Ch. 5 - 5.8 Find the positive square root of 18 using the...Ch. 5 - 5.9 Find the smallest positive root of the...Ch. 5 - 5.10 Find the positive real root of using the...
Ch. 5 - 5.11 Determine the real root of: (a) analytically...Ch. 5 - 5.12 Given
Use bisection to determine the...Ch. 5 - 5.13 The velocity v of a falling parachutist is...Ch. 5 - 5.14 Use bisection to determine the drag...Ch. 5 - As depicted in Fig. P5.15, the velocity of water,...Ch. 5 - 5.16 Water is flowing in a trapezoidal channel at...Ch. 5 - 5.17 You are designing a spherical tank (Fig....Ch. 5 - The saturation concentration of dissolved oxygen...Ch. 5 - 5.19 According to Archimedes principle, the...Ch. 5 - 5.20 Perform the same computation as in Prob....Ch. 5 - 5.21 Integrate the algorithm outlined in Fig. 5.10...Ch. 5 - Develop a subprogram for the bisection method that...Ch. 5 - 5.23 Develop a user-friendly program for the...Ch. 5 - Develop a subprogram for the false-position method...Ch. 5 - 5.25 Develop a user-friendly subprogram for the...Ch. 5 - 5.26 Develop a function for bisection in a similar...
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- 6 108 polynomial is used to approximate v8, the answer is: dy 13. of the parametric equations x: 2-3t 3+2t and y =- is dx Use the following information for Questions 14 and 15: 1+t 1+t Using the Newton-Raphson method to determine the critical co-ordinate of the graph y=f(x)=(x)*an (*) (in words x to the power of tan (x)), you will be required to determine f'(x) 14. The expression for f'(x) is: The following tools were required in determining an expression for f'(x): Application of the natural logarithm 15. I. II. The product rule III. Implicit differentiationarrow_forward1-x -2-x Evaluate So S* S* xyzdzdydx 0.arrow_forward2-the pivot value is the point of the intersection of the row of the leaving variable and the column of the solution. * true falsearrow_forward
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- The natural exponential function can be expressed by . Determine e2by calculating the sum of the series for:(a) n = 5, (b) n = 15, (c) n = 25For each part create a vector n in which the first element is 0, the incrementis 1, and the last term is 5, 15, or 25. Then use element-by-element calculations to create a vector in which the elements are . Finally, use the MATLAB built-in function sum to add the terms of the series. Compare thevalues obtained in parts (a), (b), and (c) with the value of e2calculated byMATLAB.arrow_forwardWrite the first five terms of the sequence, give the exact answer: +oo n n + 13 Determine whether the sequence converges, and if so find its limit. If the sequence diverges, indicate that using the checkbox. ai n lim n+0 n + 13 a3 The sequence diverges a4 || ||arrow_forwardfor 0 < x < 1 у (х) %3 Зех - 5 Use the Bisection Method to look for a root of the equation. Begin with values of x = 0.5 and = 0.6. Complete three iterations of the method by filling out the table below. Show your %3D calculations. Xc f(x,) f (x.) Iterations Xr 1 0.5 0.8arrow_forward
- Ex.15: Compute the temperature distribution in a rod that is heated at both ends as depicted in the following figure. Use Gauss- Seidel method given that:- T₁+2T₁+T₁_₁ = 0 where T, represents the temperature at any nodal point. Perform your calculation correct to five decimal places, and use (T = 0) as an initial guess. To = -10 °C T₁ x T₂ T3 Ts = 10 °Carrow_forwardFour different approximations are made for a solution. 1 12 13 14 4.024 3.026 2.944 2.564 As you can see the iterations are converging to 2.5. Find the magnitude of the Approximate Percent Relative Error of the third iteration. Input to your answer to the fourth decimal place.arrow_forwardUse a step size of 0.1 and round your answers to five decimal places if needed. Use Euler's method to approximate the solution x10 for the IVP y' 8y, y(0) 1. The Euler approximation for x10 isarrow_forward
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