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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).
How will you find the vertex of a parabola given in 2nd degree form (the axis of parabola is not parallel to coordinate axes)? Ans) Write the equation in type of standard form.
Tests for relative minimum For a relative minimum point there are two tests: i.The first derivative, which is (dy)/(dx) = f´(x) = 0 ii.The second derivative, which i
Perform each of the following algebraic expression as instruction says;- I.Multiply 5x+6m+4y by5 II.Divide 4ax+6ay-10az by 2a
Expected Value of Perfect Information In the above problems we have used the expected value criterion to evaluate the decisions under the conditions of risk. But, as long as un
nC6:n-3C3=91:4
The temperature in Hillsville was 20° Celsius. What is the equivalent of this temperature in degrees Fahrenheit? This problem translates to the expression 3 {[2 - (-7 + 6)] + 4
Suppose you start saving today for a $55,000 down payment that you plan to make on a house in 7 years, assume that you make no deposits into the account after the initial deposit,
The region bounded by y=e -x and the x-axis among x = 0 and x = 1 is revolved around the x-axis. Determine the volume and surface area of this solid of revolution.
Finding the Slope of a Line, Given Two Points on it ? Find the slope of the line passing through the pairs of points (-5, -2) and (2, 4). One way to find the slope is
is 4x-9 a polynomial function?
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