1. Use Matlab plots to determine how many real-valued solutions sin 2x = x has.
2. Van der Waals’ equation of state for an imperfect gas is
(v − b) = RT,
where P is the absolute pressure (atm), v is the molar volume (liter/g mole), T is the absolute
temperature (◦K), R is the gas constant (0.082054 liter atm/g mol ◦K), and a and b are
constants that depend on the particular gas. If P = 20 atm and T = 500◦K, to solve the
molar volume of carbon dioxide, use
(a) fzero (refer to Mathworks site for fzero function) to find the root,
(b) Newton’s method for which a = 3.592 liter2 atm/(g mole)2 and b = 0.04267 liter/g mole.
[Use tolerance 0.001]. You may wish to use the initial guess v0 = RT /P from the law of