Work this problem by hand. Let
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170 1
![Q1. Work this problem by hand. Let
0 1
1 0
A =
Carry out the power method with starting vector qo = [a, b]ª, where a, b > 0 and a > b.
Calculate the first few terms; what do you notice?
Explain why the sequence fails to converge. What is the problem with the convergence
argument we had in the lecture? Which of the conditions is violated?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb39617aa-1a85-4ff5-98c6-3f7fe0e80deb%2F1bc7473b-3a2f-4baf-bd51-28039917e966%2Funkpfbz_processed.png&w=3840&q=75)
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- Q1:Write (T) or (F) for the following, ,then correct the wrong one. 1- The sum of a geometric series with a=1/9 and r=1/3 equal to 1/12. 2- The sequence (1+1/n)^n diverges by the root test to (1). 3- The sequence (1+(-1)^n ) converges. 4- The speed of the velocity vector has a magnitude and direction. 5- The two parallel planes have a line of intersection. 6- Simplified component equation of the plane is Ax+By+Cz=D. 7- We calculate the cross product as a determinant. 8- The directional derivative is a number. 9- The mixed second order partial derivatives of f(x,y) denoted as f_xy or f_yx. 10- f_xx=∂/∂x (∂f/∂y).Try to prove the convergence of Newton’s MethodThe Velocity(m/s) of a body is given as a function of time (seconds) by : ds/dt =v(t) = 200ln(1+t)-t, t≥0. Determine Only the value of f(to, So) in S1 =So +hf(to, So) Where to = 2 seconds, So = 0 when using Euler's recursion method.
- For Newton's Method, y = x^d. How d will influence the convergence of Newton's method?Find the third iteration value of an extremum (maximum/minimum value) of the image if a = 4, b = 0.25, and c = 6 using Newton's Method with an initial guess value of x = - 4.7 Round off the final answer to five decimal places but do not round off on previous calculations.Solve the given exercise using the GaussSeidel method. Take the zero vector as the initial approximation and work with four-significant- digit accuracy until two successive iterates agree within 0. 001 in each variable. Compare th e number of iterations requ ired by th e Jacobi and Gauss-Seidel methods to reach such an approximate solution 2a+b=5 a-b=1
- A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 4.0 m/s, skates by with the puck. After 2.00 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.34 m/s2, determine each of the following. How long does it take him to catch his opponent? (Assume the player with the puck remains in motion at constant speed.) How far has he traveled in that time?Find the third iteration value of an extremum (maximum/minimum value) of if a = 5, b = 0.5, and c = 5 using Newton's Method with an initial guess value of x = - 4.3a. Use the 2nd-order Runge-Kutta Method to approximate y(t) with h= 0.25 b. Use the 4th-order Runge-Kutta Method to approximate y(t) with h=0.25 c. Plot both sets {yi} obtained in (1) and (2) d. Determine the eventual population level (as t→∞) reached from initial population.
- Solve the given exercise using the GaussSeidel method. Take the zero vector as the initial approximation and work with four-significant- digit accuracy until two successive iterates agree within 0. 001 in each variable. Compare th e number of iterations requ ired by th e Jacobi and Gauss-Seidel methods to reach such an approximate solution 3a + b = 1 a+ 4b+ c = 1 b + 3c = 1Find the third iteration value of an extremum (maximum/minimum value) if a = 4, b = 0.25, and c = 4 using Newton's Method with an initial guess value of x = -1.05 Round off the final answer to five decimal places but do not round off on previous calculations.Consider the convergent improper integral: ∫+∞0te^(-2)tsinh(4t)dt. If one wishes to compute its value. which Laplace transform F(s) of a certain function f(t) can be used?Select one:a. 8^s(s2-16)^2 b. 2s(s^2-16)^2 c. 2s(s^2+16)^2 d. 8s(s^2+16)^2
