Numerical Methods
4th Edition
ISBN: 9780495114765
Author: J. Douglas Faires, BURDEN
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 2.4, Problem 7E
a.
To determine
The solution of the equation using Newton’s Law, accurate to within
b.
To determine
The solution of the equation using Newton’s Law, accurate to within
c.
To determine
The solution of the equation using Newton’s Law, accurate to within
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Solvef(x) =x2−xcos(x) +14−sin2(x)4= 0,withx0=π2.(1) Does Newton’s method converge quadratically to the rootr=r1∈[0,1]? If not, explain why?(2) Find the multiplicity of the rootr=r1off(x).(3) Write out the Modified Newton’s Method such that we havequadratical convergence.
determine the radius and convergence of
E n=1 5xn/3n2
The equation e^(8−6x) − 1 = 0 has a unique solution p = 4/3. Use Newton’smethod with p0 = 1.332 to compute the next two approximations p1 and p2. If you apply Newton’s method with p0 = 2, what are p1 and p2? What comments can you make about the convergence of Newton’s method in general?
Chapter 2 Solutions
Numerical Methods
Ch. 2.2 - Use the Bisection method to find p3 for f(x)=xcosx...Ch. 2.2 - Let f(x)=3(x+1)x12(x1). Use the Bisection method...Ch. 2.2 - Use the Bisection method to find solutions...Ch. 2.2 - Use the Bisection method to find solutions...Ch. 2.2 - Sketch the graphs of y=x and y=2sinx. Use the...Ch. 2.2 - Sketch the graphs of y=x and y=tanx. Use the...Ch. 2.2 - Let f(x)=(x+2)(x+1)x(x1)3(x2). To which zero of f...Ch. 2.2 - Let f(x)=(x+2)(x+1)2x(x1)3(x2). To which zero of f...Ch. 2.2 - Use the Bisection method to find an approximation...Ch. 2.2 - Use the Bisection method to find an approximation...
Ch. 2.2 - Find a bound for the number of Bisection method...Ch. 2.2 - Prob. 12ECh. 2.2 - The function defined by f(x)=sinx has zeros at...Ch. 2.3 - Let f(x)=x26,p0=3, and p1=2. Find p3 using each...Ch. 2.3 - Prob. 2ECh. 2.3 - Use the Secant method to find solutions accurate...Ch. 2.3 - Use the Secant method to find solutions accurate...Ch. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Use the Secant method to find all four solutions...Ch. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - The fourth-degree polynomial...Ch. 2.3 - The function f(x)=tanx6 has a zero at (1/) arctan...Ch. 2.3 - The sum of two numbers is 20. If each number is...Ch. 2.3 - A trough of length L has a cross section in the...Ch. 2.3 - Prob. 17ECh. 2.4 - Let f(x)=x26 and p0=1. Use Newtons method to find...Ch. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Use Newtons method to find all solutions of...Ch. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.5 - The following sequences are linearly convergent....Ch. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.6 - Find the approximations to within 104 to all the...Ch. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Repeat Exercise 2 using Mullers method.Ch. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Two ladders crisscross an alley of width W. Each...Ch. 2.6 - Prob. 11ECh. 2.6 - Prob. 12E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- The cubic root of a number N2 can be found by solving x3 – N2 = 0 using modified secant method. Starting with x0 = 0 and taking dx = N1/N2 perform 5 iterations. Assuming the solution obtained by the calculator directly is the exact solution, calculate the true percent error in each iteration. Comment on the convergence of the method. If N1 is zero take it to be 1, if N2 is zero take it to be 11 N1=4 N2=44arrow_forwardFind the absolute error if f(x) = cos(kx) is approximated by truncating its series expansion to the first three non-zero terms if k= 3 and x = 0.445. Round off the final answer to five decimal places.arrow_forwardFind a power series for the function, centered at C and determine the interval of convergence (function is h(x) and C = 0).h(x)=1/(1-5x) Also see the attached picture of the problem.arrow_forward
- Consider the function, f(x) = x^3 − x^2 − 9x + 9. Answer the following: (a) State the exact roots of f(x).(b) Construct three different fixed point functions g(x) such that f(x) = 0. (Make sure that one of theg(x)’s that you constructed converges to at least a root).(c) Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it isconverging to?(d) Find the approximate root, x⋆, of the above function using fixed point iterations up to 4 significantfigures within the error bound of 1 × 10^−3 using X0 = 0 and any fixed point function g(x) from part(b) thatconverges to the root(s).arrow_forwardThe series ∑Cn(x+9)^n converges at x=−4 and diverges at x=−17.arrow_forwardTo find the unique solution p^∗ ∈ [0, 1] of the equation x^3 + 6x^2 − 4 = 0, rewrite the equation in the fixed-point form x = g(x) with two different choices of g, such that the sequence {pn} from the fixed-point iteration pn = g(pn−1) is expected to converge to p^∗ when p0 is sufficiently close to p^∗(but not equal to p^∗). Explain why your choices of g would work.arrow_forward
- Use Regular False Method for the following problems x cosx-2x2 +3x-1=0 within suitable interval of convergence accurate upto 5 decimal places. Give comparison with Newton’s Raphson method for reliable initial guessarrow_forwardFor what values of x does the series ∞∑n=0xn / n+1 converge?arrow_forwardSuppose that Newton’s method is applied to find the solution p = 0 ofthe equation e^x − 1 − x −1/2x^2 = 0. It is known that, starting with any p0 > 0, the sequence {pn} produced by the Newton’s method is monotonically decreasing (i.e., p0 > p1 > p2 > · · ·) and converges to 0.Prove that {pn} converges to 0 linearly with rate 2/3. (hint: use L’Hospital rule repeatedly. )arrow_forward
- Suppose that the power series ∑∞ n=0 an(x − 2)^n converges for x = 5. At which of the following points must it also converge? Choose ALL which are correct A. x = −5 B. x = −4 C. x = −1 D. x = 1 E. x = 4arrow_forwardUse Newton’s root finding method to determine the zeros for the following functions, from the starting points x0: a) f (x) = sin(x) + x^2 cos(x) − x^2 − x, x_0 = −1, and x_0 = 0 b) f (x) = x tan(x) − x, x_0 = 1, and x_0 = 2 For each starting point case, show all iterations x_1, x_2, ... x_n needed to obtain 3rd decimal precision, |f (x_n)| < 0.001. Root finding iterations may not converge, discuss why. Can you provide typed answer pleasearrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Power Series; Author: Professor Dave Explains;https://www.youtube.com/watch?v=OxVBT83x8oc;License: Standard YouTube License, CC-BY
Power Series & Intervals of Convergence; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=XHoRBh4hQNU;License: Standard YouTube License, CC-BY