Q
Using the bisection method, find the positive root of 2x(1 + x^2)^-1 = arctan x. Using
this root as x0; apply Newton'smethod to the function f(x) = arctan x: Interpret
the results you obtain.

Please see the attached file for the fully formatted problem.
The equation x2 - 3x + 1 = 0 has a solution for x>= 0. Give the third approximationby using Newton'smethod. Your first approximation is to be 1.

3. (Rootfinding andOptimization)
(a) Suppose that f is differentiable on [a, b]. Discuss how you might use a rootfinding method to identify a local extremum of f inside [a, b].
(b) Let f(x) = logx ? cosx. Prove that f has a unique maximum in the interval [3,4]. (NB: log means natural logarithm.)
(c) Approximate this local ma

Referring to the table in the attached table, consider that hiring a driver costs $10 while each machine costs $100. Which method should he use and why?
See attachment

The NewtonsSquareRoot Class
Objectives
? Writing a class using conditionals that test double values
? Writing a class using a while loop
The project directory should include the following:
? NewtonsSquareRoot.java
? NewtonsSquareRootTest.java
Details
To approximate the square root of a positive number n using Newton

Accodting to Newton's universal law of gravity, if the separation between to bodies is increased by a factor of three, the gravitational pull each has on the other will be X by a factor of Y ?

Do explain the process of Normalization?
Explain the context in which Normalization is used?
What is its purpose?
What are the steps to be taken?
What do we actually do when we normalize?
Would you describe Normalization as Science or Art?
Dedicate your last paragraph to Optimization (de-normalization)