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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:
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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).
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Consider the Solow growth model as given in the lecture notes using the Cobb-Douglas production function Y t = AK 1-α t L α t a) Set up the underlying nonlinear differen
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Write a function that computes the product of two matrices, one of size m × n, and the other of size n × p. Test your function in a program that passes the following two matrices t
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A triangle has vertices A (-1, 3, 4) B (3, -1, 1) and C (5, 1, 1). The area of ABC is a) 30.1 b) 82.1 c) 9.1 d) 52.1
What are the key features of Greek Mathematics? How does the emphasis on proof affect the development of Greek Mathematics?
what is a sample space diagram
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