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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).
Your bank has a loan outstanding with a current balance of $1,000,000 that is payable in quarterly equal instalments of $49,924. This loan has another 6 years to maturity. The bo
Evaluate both of the following limits. Solution : Firstly, the only difference among these two is that one is going to +ve infinity and the other is going to negative inf
1. The polynomial G(x) = -0.006x4 + 0.140x3 - 0.53x2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase
Proof for Properties of Dot Product Proof of u → • (v → + w → ) = u → • v → + u → • w → We'll begin with the three vectors, u → = (u 1 , u 2 , ...
A small airplane used 5and2over3 gallons of fuel to fly a 2 hour trip.how many gallons were used each hour
approximate the following problem as a mixed integer program. maximize z=e-x1+x1+(x2+1)2 subject to x12+x2 =0
While we first looked at mechanical vibrations we looked at a particular mass hanging on a spring with the possibility of both a damper or/and external force acting upon the mass.
A piece of cardboard in the shape of a trapezium ABCD & AB || DE, ∠ BCD = 900, quarter circle BFEC is removed. Given AB = BC = 3.5 cm, DE = 2 cm. Calculate the area of remaining p
how will the decimal point move when 245.398 is multiplied by 10
Launching a new product (Blackberry Cube) Analysis (target market) Product features Promotions and advertisement sample design (location)
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