With the use of Newton's method, we would like to determine the fourth root of 200 by finding the numerical solution of the equation x4 − 200 = 0 with the start x0 = 8. When carrying out the first three iterations, write down x3 in the below blank. (Use 5 significant digit when calculating manually, for example, 2.34012→2.3401)

With the use of Newton's method, we would like to determine the fourth root of 200 by finding the numerical solution of the equation x4 − 200 = 0 with the start x0 = 8. When carrying out the first three iterations, write down x3 in the below blank. (Use 5 significant digit when calculating manually, for example, 2.34012→2.3401)

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids

Section: Chapter Questions

Problem 79A

See similar textbooks

Related questions

Q: Use Newton's method with initial guess x1 = 1 to compute two successive approximations of the…

Q: Apply Gauss-Seidel method to solve the values of the x as given. Continue iterations until two…

A: Basic information: Put: A = x1 ; B = x2 ; C = x3…

Q: i. Find the real root of the given function f(x) = e²¹ − x −6=0 by Newton-Raphson iterative method…

Q: Write the formula for Newton’s method and use the given initialapproximation to compute the…

A: We first find f'(x)

Q: i) Maktoum was using iterative methods to solve equations in MATLAB. For the equation f(x) = x³ + 5x…

A: According to the given information, it is required to approximate the third iteration according to…

Q: 1- Using Newton-Raphson method solve xlog, x=12.36 with Na - 10, to 3 iterations? 2- Find the real…

Q: Use Newton's method to find an approximate solution of In (x) = 8 – x. Start with xo = 4 and find…

Q: 3. Find the roots using newton using initial guess 5.4 with an accuracy of 1% f(x) = -0.676x10x*…

A: Newton Method:- For a function f(x) method is xn+1=xn-fxnf'xn; n=0, 1, 2,... Given that…

Q: Use Newton’s method to estimate the one real solution ofx3 + 3x + 1 = 0. Start with x0 = 0 and then…

A: x3+3x+1=0

Q: Find the solution of the equation In (2x-1)+cos (π/4 x-1) = 1.7 using Newton-Raphson method with an…

Q: Which of these initial approximations does not work when using Newton's method to find the roots of…

A: For the Netwon method, f'(x) should be non zero.

Q: Use False Position Method. • Compute Es according to 4 significant figures according to the formula…

A: Given function is fx=2x cos 2x-x-22 defined on the interval 2,3. To determine: 1) One real root of…

Q: 2. Show that the equation xe = 1 has a root between 0.5 and 0.6. starting with 0.55 as a first…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1- Using Newton Raphson method solve xloB *= 12.36 with xa= 10, to 3 iterations? 2- Find the real…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Approximate the positive root of the equation x – sinx-1=0 , by performing five iterations of the…

Q: Find root by using Newton Raphson method, x-sinx/4-1/2=0,with x_o=0.5

A: Finding the root equation f(x)=0. Take the initial approximation x=x0 First approximation is given…

Q: 5) Solve the PDE by reducing it to normal form xuxx-yuxy = 0. (CO2)

A: Since you post more than one non interlinking questions as per our guideline we can solve only first…

Q: Solve 2x cos2x + 3 = (x - 2)² using Newton-Raphson Method and an intial value of 1 with an error…

A: The given problem is to find the approximate root of given equation using newton raphson method with…

Q: Use (a) Fixed Point Iteration method (b) Newton-Rhapson method and (c) Secant Method to find the…

A: As per the guidelines, since there are more than one questions only one question will be answered.…

Q: Determine the fourth root of 200 by finding the numerical solution of the equation x^4 − 200 = 0.…

A: x4-200=0x0=8To carry out the first five iterations

Q: Use Newton’s method to find an approximate solution of xex = 1. Start with x0 = 0 and find x2.

A: Given equation:

Q: Solve one real root of e* – 2x – 5 = 0 with xo = -2 using the Fixed-Point Iteration Method |…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Q/1 Find the root of eq:- (X-1) = X+8 by N-R method correct to 2D. Use X0-4 Q2/ Find the square root…

A: Newton Raphson Method : Suppose we need to solve the equation f(x)=0 and x=c is the actual root…

Q: Find solution of the equation x2 = 17 by the Newton's method.

A: We find the solution of x2=17 by Newton's method.

Q: Use Newton's method to find an approximate solution of In (x) = 8 – x. Start with xo = 4 and find…

Q: 3. Solve xex- 3 = 0, correct to three decimal places by using the Newton- Raphson method.

A: Here, fx=xex-3⇒f'x=xex+ex f1=1*e1-3=-0.2817<0 f2=2*e2-3=11.778>0 Thus root lies between 1 and…

Q: Sketch on the same coordinate axes, the graphs of y-(x-1) and y=- x-2 Hence, deduce the number of…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use Newton's method to approximate a root of the equation 2x+ 3x+2=0 as follows: Let 1=-2 be the…

Q: Determine the fourth root of 200 by finding the numerical solution of the equation = 8 and carry out…

A: Let fx=x4-200. The derivative of fx=x4-200 is, f'x=ddxx4-200=4x3 By Newton-Raphson method,…

Q: Use Newton's method to find an approximate solution of In (x)= 6- x. Start with xo = 7 and find x2.…

Q: | 3. Solve 3x - cosx – 1 = 0, correct to three decimal places by using the Newton-Raphson method.

Q: Solve 2x + cos x = 5 using Newton-Raphson method and an initial value of with an error less than 5%.…

A: Newton Raphson method Steps Step-1: Find points a and b such that a<b and f(a)⋅f(b)<0.…

Q: Use Newton's method to approximate a root of the equation 4x' + 4x + 4 = 0 as follows. Let x1 = 3 be…

Q: 1. Use the Regula-Falsi Method to solve for one real root of sin x – x³ on the interval (0.50,1)…

Q: Approximate the positive root of the equation x -sinx-1=0 , by performing five iterations of the…

Q: Find the Newton's formula (X₂+1 in terms of xn) for calculating the cube root of R. Calculate two…

Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ] using numerical…

Q: Approximate the root of the equation x5 – 5x – 4 = 0, beginning xo = 1.6, and continuing until two…

A: For the solution of the problem follow the next step.

Q: 2. Determine one real root of 8 (sin æ) e- - 1 = 0 with æo = 0.30 using three iterations of Newton-…

Q: Apply Gauss-Seidel method to solve the values of the x as given. Continue iterations until two…

Q: 25: Find the root of the equation f(x) = x3 – 4x + 1 giving the answer to s decimal places, by using…

A: Given: f(x)=x3-4x+1

Q: 4. Find the smallest positive root of the equation a-r-10 = 0 using Newton Raphson method correct to…

A: Let fx=x4-x-10 ⇒f'x=4x3-1 Now f1=-10<0, f2=4>0 As f1f2<0 So, by Intermediate value theorem…

Q: 3 Use Newton's method to approximate a root of the equation 5x + 7x + 2 = 0 as follows. Let 31 2 be…

Q: 12 Show that the equation (5– 3x)i = x has a root in the interval (1,2) . By using the…

A: Step:-1 Newton Raphson Method:- xn+1=xn-fxnf'xn Given that 5-3x13=x 5-3x13=x⇒5-3x13 -x =0 Take…

Q: Q5: Find the root of the equation f(x) =x3 – 4x + 1 giving the answer to 5 decimal places, by using…

A: Using two methods,

Q: Solve one real root of e* – 2x – 5 = 0 with xo = -2 using the Fixed-Point Iteration Method until…

Q: Find the positive real root of x³ - x - 3 = 0 using Newton-Raphson method. If the starting guess…

Q: Find a root of the x^4-27=0 equation using the Newton Raphson method (in 4 steps)

A: The given equation is x4-27=0. Let fx=x4-27. Then, f'x=4x3 Here, f2=24-27=16-27=-11<0…

Question

With the use of Newton's method, we would like to determine the fourth root of 200 by finding the numerical solution of the equation x⁴ − 200 = 0 with the start x₀ = 8. When carrying out the first three iterations, write down x₃ in the below blank. (Use 5 significant digit when calculating manually, for example, 2.34012→2.3401)

Expert Solution