Using Newton Raphson Method in Excel, Given: f(x) = e^x - 3x^2 = 0, how many iterations would you take to get the root between [0, 1] with an error less than 0.00000001. (A) 4 B) 6 C) 8 2
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- Solve the equation f (x) = x2 + ln x - 3 = 0 using the fixed point method. Detail the steps of iterative calculations. Discuss the results. (Convergence to 8 decimal places).data point at x1= 1, x2=4, x3=6 and x4=5 were used to estimate ln 2 with a third-order newtons interploting polynomial f(x)=lnx solved this according to numerical analysisIn a factory there is a 10,000 liter water tank that contains 0.01% colorant. From the beginning (t = 0) water with a dye content of 0.001% is pumped into the tank at a rate of 4 l/min. The water leaves the tank at the same speed. Calculate the percentage of chlorine in the tank after 60 minutes (iterations) taking time intervals of one minute: - using the approximate method of Euler and Runge Kutta of 4 order.
- Approximate root of the function y = f (x) was calculated with the initial value given by the Newton-Raphson method and the data in the table was obtained. Accordingly, which of the following is the first iteration that gives the correct result for 2 significant steps?Determine the root of the function ln (x2) = 7 a. Analytical solution of 3 decimal-point accuracy b. Bisection Method using [1, 2] and stop when error is less than 0.1%. Use 3 decimal points accuracy.A golfer makes a successful chip shot to the green. Suppose that the path of the ball from the moment it is struck to the moment it hits the green is described by y = 12.54x −0.41x² where x is the horizontal distance (in yards) from the point where the ball is struck, and y is the vertical distance (in yards) above the fairway. Use a CAS or a calculating utility with a numerical integration capability to find the distance the ball travels from the moment it is struck to the moment it hits the green. Assume that the fairway and green are at the same level and round your answer to two decimal places.
- integral from -5 to 4 of absolute x^2-4 dxSolve for y2 by using reduction of order And for nonhomogeneous using undetermined coefficients linear mathematicsFind the work done in emptying the tank in example 4. If the tank water is pumped to a level 1.00 meters above the top of the tank and the water is initially 4.00 meters deep.
- b) Calculate the general solution in implicit form of the equation c) Find the particular solution that passes through the point (2, -√ln2) and the interval where maximal is definedFind the root of the equation fx=ln(x)-5+x in the interval [3.0, 4.0] using Regula Falsi method. Use percent relative error control 0.2% (Error_ra(%)=100*|xk-xk-1|/|xk|). Use at least 5 decimal places in your calculations.Integrals to be evaluated directly and using a series approximation.