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I have gone over these problems and I am stuck. If anyone can help me at any part of this, it will be appreciated.

4.3.1 Convergence of the bisection method
Implement the bisection method in a computer code, and compute the roots of the quadratic equation
x2 &#8722; 2 x + 0.9 = 0. Prepare and discuss a graph of the error against the iteration count, k.

4.5.2 Newton&#8217;s method
(a) Compute all zeros of the function f(x) = ln |x|+3&#8722;3.1 x2, accurate to the eighth decimal place.
Explain your choice of initial guess.

4.5.3 More on Newton&#8217;s method
(a) The function f(x) = x ln x has a root at x = 0. What is the rate of convergence of Newton&#8217;s
method toward this root?

4.5.4 Redlich-Kwong equation of state
Write a program that produces and prints a table showing the molecular volume of hydrogen for
fifteen combinations corresponding to pressure p = 1, 2, 3, 4, and 5 atm and temperature T = 200,
300, and 400 &#9702;K, based on the Redlich-Kwong equation of state (4.1.10). For the initial guess, use the
predictions of the ideal gas law. Discuss the physical significance of your results. Perry&#8217;s Chemical
Engineer&#8217;s Handbook (McGraw-Hill, fifth edition, pp. 3&#8211;41, 3&#8211;104) gives the following information
for hydrogen: Chemical formula: H2; Boiling Point at 1 atm: &#8722;252.7&#9702;C; critical conditions: Tc =
&#8722;239.9&#9702;C; Pc = 12.8 atm.

4.5.5 Viscous flow in a corner
The nonlinear equation
sin[2(x &#8722; 1)] = (1 &#8722; x) sin(2), (1)
describes viscous flow in a corner bounded by two intersecting walls with aperture angle 2; the
variable x is a measure of the strength of the flow. A trivial solution for any  is x = 1. Find and
plot another solution branch, X(), in the range 0 <  < .

4.6.4 A system of two equations
Compute one solution of the system
(x &#8722; 2)2 + (y &#8722; 3)3 + (x &#8722; 2.1)(y &#8722; 3.1) = 2.81, 10 e&#8722;x + 5 e1&#8722;y = 0.7468, (1)
using (a) Newton&#8217;s method, and (b) Newton&#8217;s method with the Jacobian evaluated only at the
beginning and then held constant. Compare the respective rates of convergence.