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1. Write two m-files, one for the bisection method and another for Newton's method.
2. Using both the Bisection method and the Newton method answer the following:
Include the commands you typed into Matlab
a) Find the root to 3, 5, and 8 decimal places of f(x) = x2- 2 starting with an initial approximation of x=1.
b) How many steps did it take for the bisection method to find the root to 3, 5, and 8 decimal places?
c) How many steps did it take for the Newton method to find the root to 3, 5 and 8 decimal places?
3. Use Newton's method to find all the real roots of f(x) = x5+ x4 -4x3 - 3x2- 3x +1
4. Apply Newton's method to the function f(x) = x3 - x with an initial approximation of x=1/√5. Is the method converging? What happens? Explain your answer using the graph of f(x).
5. Use Newton's method on the function (x) = 3√5 . What happens when your initial approximation is not x=0? Explain your answer using the graph of f(x).
Write the subsequent 2nd order differential equation as a system of first order, linear differential equations. 2 y′′ - 5 y′ + y = 0 y (3) = 6 y′ (3) = -1 We can wri
find the matrix of the linear transformations T:R2->R2 defined by T(x,y,z)=(x+2y,x-3z).
A tangent to a curve at a point is a straight line which touches but does not intersect the curve at that point. A slope of the curve at a point is defined as the
How Does The Algorithm Work? Most of us, when asked to multiply, say, 35 by 23, write Why do we place the mark x (or 0, or leave a blank) in the second row of the calcul
suresh invested rs.1080 in shares of face value rs.50 at rs.54.After receiving dividend on them at 8% he sold them at 52.In each of the transaction he paid 2 % brokerage.Hpw much d
From past experience a machine is termed to be set up correctly on 90 percent of occasions. If the machine is set up correctly then 95 percent of good parts are expected however i
A police academy is training 14 new recruits. Some are working dogs and others are police officers. There are 38 legs in all. How many of each type of recruits are there?
How do you do converting metric units?
give an example of a binomial of degree 27?
It is the full blown case where we consider every final possible force which can act on the system. The differential equation in this case, Mu'' + γu' + ku = F( t) The displ
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