Quiz Chapter 03.03: Bisection Method of Solving a Nonlinear Equation

1. The bisection method of finding roots of nonlinear equations falls under the category of a(n) _____ method.

2. If for a real continuous function f(x), you have f(a) f(b) < 0, then in the interval \left[ a,b \right] for f(x) = 0, there is (are)

3. Assuming an initial bracket of \left[ 1,5 \right], the second (at the end of 2 iterations) iterative value of the root te^{-t} - 0.3 = 0 is

4. 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

5. For an equation like x^{2}=0, 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 f(x)= x^{2}

6. The Ideal Gas Law is given by

pv=RT

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

\left( p + \dfrac{a}{v^{2}} \right) \left( v-b \right) = RT

where a and b are empirical constants dependent on a particular gas. Given the value 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?