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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).
Estimation of difference among population proportions Assume the two proportions be described by P1 and P2, respectively,Then the difference absolute between the two proportion
Tangent Lines : The first problem which we're going to study is the tangent line problem. Before getting into this problem probably it would be best to define a tangent line.
1. Find the number of zeroes of the polynomial y = f(x) whose graph is given in figure. 2 Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0) and (7,-6).
what are the formulas in finding the perimeter of a plane figure?
Telescoping Series It's now time to look at the telescoping series. In this section we are going to look at a series that is termed a telescoping series. The name in this c
to plot (5,-4), start at (0,0) and move 5 units left and 4 units down
1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
Here we know x can only be 1 or -1. so if it is 1 ans is 2. if x is -1, for n even ans will be 2 if x is -1 and n is odd ans will ne -2. so we can see evenfor negative x also an
why is multiplying inportent in our lifes
Which of the following is the most crucial aspect of learning multiplication? i) Multiplication facts ii) Recall of tables and their recitation iii) Understanding "how man
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