Holistic Numerical Methods Institute
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Multiple Choice Test
Bisection Method
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 xl and xu, 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 x2=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)=x2 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
pv=RT
where where 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
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