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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).
Evaluate the linear equation: Solve the equation ax - b = c for x in terms of a, b, and c. Solution: Step 1. Using Axiom 1, add b to both sides of the equation. a
Pai is rational or irrational
Trace the curve y 2 = (x + 2) 2 (x - 6). Clearly state all the properties you have used for tracing it(e.g., symmetry about the axes, symmetry about the origin, points of interse
Find the values of x and y
Simple derivatives Example Differentiate following. (5x 3 - 7 x + 1) 5 ,[ f ( x )] 5 ,[ y ( x )] 5 Solution: Here , with the first function we're being asked to
explain how business mathematics in an inbu;it component of a payroll package
1. A drainage system overflows into a river causing pollution when the rainfall falling in an hour exceeds 50 mm. During any given year, the maximum hourly rainfall follows an expo
11/20=
Objectives After studying this leaarn maths; you should be able to explain why a teacher needs to know the level of development of hi; her learners; identify the way
Utilizes the definition of the limit to prove the given limit. Solution In this case both L & a are zero. So, let ε 0 so that the following will be true. |x 2 - 0|
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