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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).
Suppose that we know the logarithms of all numbers which are expressed to base 'a' and we are required to find the logarithms of all these numbers to base 'b'. We
Q. How to Subtract fractions with the same denominators? Ans. Subtracting fractions is basically the same as adding them. If you don't know how to add fractions, you shoul
Fermat's Theorem If f(x) has a relative extrema at x = c and f′(c) exists then x = c is a critical point of f(x). Actually, this will be a critical point that f′(c) =0.
i have question like proof, can you please help me on it?
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The Geometric Index or Industrial Share index The Geometric Index or Industrial Share index is an index of 30 selected top industrial companies. This is calculated by taking a
What is the LCM of 4, 6, 18
Tom has five times as many marbles as Jim. together they have 42 marbles. how many marbles does each has?
a) Write a summary on Tower of Hanoi Problem. How can it be solved using recursion ? b) Amit goes to a grocery shop and purchases grocery for Rs. 23.
Find the area of a circle along with a radius of 6 inches. The formula for the area of a circle is A = πr 2 . Use 3.14 for π. Substitute 6 for r in the formula A = πr 2 and solve
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