Quiz Chapter 03.03: Bisection Method of Solving a Nonlinear Equation


(All Tests)


(More on Bisection Method)


(More on Nonlinear Equations)

Pick the most appropriate answer

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


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?