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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).
Find the perimeter of the figure, where AED is a semi-circle and ABCD is a rectangle. (Ans : 76cm) Ans: Perimeter of the fig = 20 + 14 + 20 + length of the arc (AED
f(x)=ex -3x
Interpretations of the Derivative : Before moving on to the section where we study how to calculate derivatives by ignoring the limits we were evaluating in the earlier secti
Eileen needs 9 feet of fabric to make a skirt. If Eileen has 18 feet of fabric how many skirts can she make?
Optimization : In this section we will learn optimization problems. In optimization problems we will see for the largest value or the smallest value which a function can take.
If 4x^4+9x^4=64 then the maximum value of x^2+y^2 is solution) From the eq. finding the value of x^2 and putting it in x^2 + y^2.we get 2nd eq. differentiating that and putting
Evaluate following limits. Solution: Let's begin this one off in the similar manner as the first part. Let's take the limit of each piece. This time note that since our l
Jennifer ?ipped a coin three times and got heads each time. What is the probability in which she gets heads on the further ?ip? The probability of heads does not modify based o
If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.
A 65 ohm resistor is connected to a power supply , a current of 2.4 amperes is drawn. what is the output voltage?
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