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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).
Mona purchased one and a half pounds of turkey at the deli for $6.90. What did she pay per pound? Divide the cost of the turkey by the weight; $6.90 ÷ 1.5 = $4.60.
2(x+3x)+(x+3x)
Determine or find out if the following series is convergent or divergent. Solution In this example the function we'll use is, f (x) = 1 / (x ln x) This function is
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differentiate x to the power 3
Carmen bought 3 pounds of bananas for $1.08. June paid for her purchase of bananas. If they paid the same price per pound, how many pounds did June buy?
Even and Odd Functions : This is the final topic that we have to discuss in this chapter. Firstly, an even function is any function which satisfies,
Rule 1 The logarithm of 1 to any base is 0. Proof We know that any number raised to zero equals 1. That is, a 0 = 1, where "a" takes any value. Therefore, the loga
Find the sum of all natural numbers amongst first one thousand numbers which are neither divisible 2 or by 5 Ans: Sum of all natural numbers in first 1000 integers which ar
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