9) Consider the nonlinear equation (x - 1)(x-2)³ = 0. Use the modifiedNewton's method used for computing a root whose multiplicity is knownand compute r₁ and r2 with ro = 2.25. Then x1 + x₂ =Hint: The iterative sequence converges to the root r = 2.]

The equation is (x-1)(x-2)3 = 0. Clearly, it's roots are 1 (with multiplicity 1) and 2 (with…

Answered: 9) Consider the nonlinear equation (x -…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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14. Use Newton's method to find the root of the equation x5 – 3x4 + 7x² – 3x – 2 = 0 in the closed interval [-1,0]. For x1 = -0.5, find x2 and x3 and sketch the graph. Round to three decimal places.
Q2 (a) Azli and Iman are both traveling for Batu Pahat to Melaka on daily basis. The average travelling time for both them is 98.4 minutes with a standard deviation of 7.8 minutes and 110.7 minutes with standard derivation of 29.8 minutes respectively. Assume that the traveling population are approximately normal distributed and random samples of traveling time of Azli and Iman are 36 and 49 respectively. (i) Calculate the probability of Azli's average travelling time to be more than 100 minutes. (ii) Find the probability of Iman's average travelling time to be in between 105 and 115 minutes.
21. (a) Use Newton's method to find the root of the equation r – xª + 3x2 – 3x – 2 = 0 in the interval [1,2] correct to six decimal places. (b) Use Newton's method to find the root of the equation 3x4 – 8x3 +2 = 0 in the interval [2,3] correct to six decimal places. 22. A particle is moving with the given data. Find the position of the particle. (a) v (t) = 3t – R, s (0) = 1. (b) a (t) = 2 sint + 3 cos t, s (0) = 0, v (0) = 2. 1+t² >
is question has several parts that must be completed sequentially. If you skip a part of the question, you will not rec rt, and you will not be able to come back to the skipped part. Tutorial Exercise If a rock is thrown upward on the planet Mars with a velocity of 16 m/s, its height above the ground (in meters) after t seconds is given by H = 16t - 1.86t. (a) Find thevelocity (in m/s) of the rock after 1 second. (b) Find the velocity (in m/s) of the rock when t = a. (c) When (in seconds) will the rock hit the surface? (d) With what velocity (in m/s) will the rock hit the surface? Click here to begin! Need Help? Read It Show My Work (Optional) 3?
A car and a truck leave the same place and travel in the same direction along a straight road. The car starting from rest speeds up to 24 kph with a constant acceleration of 1/6 m/s² and then runs at this speed. The truck leaves 40 seconds after the car with a uniform acceleration of 1/3 m/s² from rest to attain a speed of 48 kph and then travels at this speed. How soon after the car started will the truck overtake the car?
Q7 a) A population of insects at a rate of 200+10t+0.25t² insects per day (t in days). Find the insect population after 3 days, assuming that there are 35 insects at t = 0. b) The traffic flow rate past a certain point on a highway is q(t) = 3000 + 2000t - 300t2 (t hours), where t= 0 is 8 AM. How many cars pass by in the time interval from 8 AM to 10 AM?
3.) Determine the root of the equation by Secant Method (should converge at three decimal places b.) f(x)= ex-4, Xạ=1.5, Xb=1.2

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9) Consider the nonlinear equation (x - 1)(x-2)³ = 0. Use the modified Newton's method used for computing a root whose multiplicity is known and compute ₁ and ₂ with o = 2.25. Then x1 + x^₂ = [Hint: The iterative sequence converges to the root r = 2.]