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Question 7 [10 points) Show that there is a root of the equation sin(x) = x?...
Please answer all questions
Q2 2015
a) show that the function f(x) = pi/2-x-sin(x)
has at least one root x* in the interval [0,pi/2]
b)in a fixed-point formulation of the root-finding problem, the
equation f(x) = 0 is rewritten in the equivalent form x = g(x).
thus the root x* satisfies the equation x* = g(x*), and then the
numerical iteration scheme takes the form x(n+1) = g(x(n))
prove that the iterations converge to the root, provided that
the starting...
Use the Intermediate Value Theorem (IVT) to show that there is a root of the equation in the given interval (a) x -+3x – 5 = 0 (1,2) (b) 2sin(x) = 3 -2x. (0.1)
QUESTION 1 (a) Show that the equation (x - 2) = has a root between x = 2 and x = 3. Using the x+2 first approximation as 2.7 and the Newton-Raphson method, calculate this root correct to two decimal places. (8 marks) (b) Show that e' +x-2 = 0 has a root in interval [0, 1]. Using basic iteration method, calculate this root correct to four decimal places. (12 marks) 1 (C) Find an approximate value for the integral...
Please use Taylor Polynomial series and quadratic formula.
8. (10 points) Consider the equation cos(x)-x = 0. The plot of y-cos(x)-x reve that the equation has a single root lying in the interval [0, 1] (marked with a circle). 0.5 0 0.8 -0.5 0.6 0.4 0.2 Find the best possible approximation for that root.
8. (10 points) Consider the equation cos(x)-x = 0. The plot of y-cos(x)-x reve that the equation has a single root lying in the interval [0,...
3、0-11 points SEssCalcET2 4 6 013. Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The root of x-2x3x2-9-0 in the interval [1,2] Read It Watch t Talk to a Tutor
3、0-11 points SEssCalcET2 4 6 013. Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The root of x-2x3x2-9-0 in the interval [1,2] Read It Watch t Talk to a Tutor
sin x 2. a. Show that x = 3+ has a solution in the interval [3,4]. 2 b. How many iterations of the Bisection Method are needed to solve the equation with the accuracy E= 10-1 c. Find the root of equation above to the accuracy within 1€= 10-1 using Bisection Method. . Directions: Use the radian mode on your calculator when using the trigonometry buttons. • Use five-digit rounding arithmetic in your calculations
PLEASE explain and show work?
5. (30 points) Use the secant method to find a root of the following equation with two initial guesses xo 2.x1 1.8. Please show the first two iterations only. f(x) = 1-x + sin(x)
6 & 7
5 points. Solve the equation for solutions in the interval (0,271). 1 6) sin x cos X= 5 points. Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary. 7) sin2e - sin 0 - 12 = 0 7
QUESTION 6 The equation X +in(x) = 0 has one root in the interval Oa (0.5, 0.6] b.10.2, 0.3] Os [2, 3] , (5,6] QUESTION 7 The method for solving the system of nonlinear equations is a Gauss-Seidel b. Cramer's rule Newton-Raphson method d. Bisection method QUESTION 8 In linear programming problems, all variables must assume non-negative. True
Using the Bisection method, find an approximate root of the equation sin(x)=1/x that lies between x=1 and x=1.5 (in radians). Compute upto 5 iterations. Determine the approximate error in each iteration. Give the final answer in a tabular form.