Q1. The bisection method of finding roots of nonlinear equations falls under the category of a (an) ______ method.

open
bracketing
graphical

random

Q2. If
for a real continuous function f(x), you have f(a)f(b)<0, then in the
interval [a,b] for f(x)=0, there is (are)
one root
an undeterminable
number of roots
no root
at least one root

Q3. Assuming
an initial bracket of [1,5] , the second (at the end of 2 iterations) iterative value of the root of
is
0.0
1.5
2.0
3.0

To find the root of f(x)=0, a scientist uses the bisection method. At the
beginning of an iteration, the lower and upper guesses of the root are x_{l} and
x_{u}, respectively. At the end of this iteration, the absolute relative
approximate error in the estimated value of the root would be

For an equation like
, a root exists at x=0. The bisection method cannot be
adopted to solve this equation in spite of the root existing at x=0 because the function
is a polynomial
has repeated roots
at x=0
is always
non-negative
has
a slope of zero at
x=0

The ideal gas law is given by

where where p is the pressure, v is the specific volume, R is the
universal gas constant, and T is the absolute temperature.
This equation is only accurate for a limited range of pressure and
temperature. Vander Waals came up with an equation that was accurate for
larger range of pressure and temperature given by

where a and b are
empirical constants dependent on a particular gas. Given the value of
R=0.08, a=3.592, b=0.04267, p=10 and T=300 (assume all units are consistent), one is
going to find the specific volume, v, for the above values. Without
finding the solution from the Vander Waals equation, what would be a good
initial guess for v?
0
1.2
2.4
4.8