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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 given definite integral. Solution Let's begin looking at the first way of dealing along with the evaluation step. We'll have to be c
Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections. Two vectors are parallel if they have
At a point in a loaded member, the stresses relative to an x, y, z coordinate system are given by Calculate the magnitude and direction of the maximum principal stress.
E1) From your experience, and what you have studied so far, by which age would-you expect an average child to be ready to acquire the following concepts? i) Simple classificatio
give some examples of fractions that are already reduce
HE IGHTS AND DISTANCES If the angle of elevation of cloud from a point 'h' meters above a lake is α and the angle of depression of its reflection in the lake is β , prove
Graph y = tan ( x ). Solution In the case of tangent we need to be careful while plugging x's in since tangent doesn't present wherever cosine is zero (remember that tan x
What kinds of classroom activities can you think of for helping children to make groups of 5 and 10? Once they have enough practice with such activities, children can be helped
32gal/min = qt/hr
Sums and Differences of Cubes (and other odd powers)? You can factor a sum or difference of cubes using the formulas a 3 - b 3 = (a - b )(a 2 + ab + b 2 ) and a 3 + b 3 =
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