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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).
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A lotus is 2m above the water in a pond. Due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of 10m from the original positio
a. Estimate the following model, C t = β 0 + β 1 * DI t + ε t Where C t = Aggregate Consumption Expenditure in Australia, quarterly data for the per
uses of maths concept
As1212uestion #Minimum 100 words accepted#
Consider the integral where the notation means a contour that is parallel to the real z axis, but moved down by a distance d . Use the method of steepest descents to deri
One integer is two more than another. The sum of the lesser integer and double the greater is 7. What is the greater integer? Let x = the greater integer and y = the lesser int
The interval of validity for an IVP along with initial conditions: y(t 0 ) = y 0 or/and y (k) (t 0 ) = y k There is the largest possible interval on that the solution is va
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
What is the square root of -i and argument of -i Ans) argument of -i is 270 ad 1 is the square root of -i
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