Question: The velocity of a body is given by the following equation 

v(t) = te^-t+ 1/t 

where 

     is given in seconds and v is given in m/s 

  Find the time when the velocity of the body will be 0.35 m/s. Use bisection method  and conduct three iterations. Use initial bracketing guess of [1,8]. Show all steps in calculating the estimated root, absolute relative approximate error and the velocity of  the body for each iteration. Also, tabulate your answers as  iteration number, estimated root, absolute relative approximate error, and velocity of the body.

Problem Set 

chapter 3.04

NewtOn- Raphson  Method of Nonlinear Equations 
Question 1.  Find the estimate of the root of x2 — 4 = 0 .by using Newton-Raphson method ,if the initial guess of the root is 3. Conduct three iterations. Also, calculate the approximate error, true error, absolute relative approximate error, and absolute relative true error at the end of each iteration.

Question 4. The root of the equation f (x) = 0 is found by using the Newton-Raphson method ,if  the initial estimate of the root is assumed to be x0=3 given f(3)=5 and the angle the tangent makes to the function f (x) at x  = 3 is 57°, what is the next estimate  of the root, x1? 

Question 5. The root of the equation f(x) = 0 is found by using Newton-Raphson method. The initial estimate of the root is assumed to be xo = 5.0 , and the angle the tangent makes with the x -axis to the function f (x) at xo = 5.0 is 89.236° . If the next estimate of the root is, x1= 3.693 , what is the value of the function f (x) at x =5?