Quiz Chapter 03.05: Secant Method of Solving Nonlinear Equations

1. The secant method of finding roots of nonlinear equations falls under the category of _____ methods.

bracketing

graphical

open

random

2. The secant method formula for finding the square root of a real number $R$ from the equation $x^{2} - R = 0$ is

\dfrac{x_{i} x_{i-1} + R}{x_{i} + x_{i-1}}

\dfrac{x_{i} x_{i-1}}{x_{i} + x_{i-1}}

\dfrac{1}{2} \left( x_{i} + \dfrac{R}{x_{i}}\right)

\dfrac{2 {x_{i}}^{2} + x_{i} x_{i-1} - R}{x_{i} + x_{i-1}}

3. The next iterative value of the root of $x^{2} - 4 = 0$ using secant method, if the initial guesses are $3$ and $4$ , is

2.2857

2.5000

5.5000

5.7143

4. The root of the equation $f(x) = 0$ is found by using the secant method. Given one of the initial estimates is $x_{0} = 3$ and $f(3) = 5$ , and the angle the secant makes with the function $f(x)$ is $57^{\circ}$ , the next estimate of the root, $x_{1}$ , is

-3.2470

-0.24704

3.2470

6.2470

5. For finding the root of $\sin{\left( x \right)} = 0$ , the following choice of initial guesses would not be appropriate.

\dfrac{\pi}{4}

and

\dfrac{\pi}{2}

\dfrac{\pi}{4}

and

\dfrac{3 \pi}{4}

-\dfrac{\pi}{2}

and

\dfrac{\pi}{2}

\dfrac{\pi}{3}

and

\dfrac{\pi}{2}

6. When drugs are given orally to a patient, the drug concentration $c$ in the blood stream is given by a formula $c=Kte^{-at}$ where $K$ is dependent on parameters such as the dose administered while $a$ is dependent on the absorption and elimination rates of the drug. If $K=2$ and $a=0.25$ , where $t$ is in seconds and $c$ is in mg/ml, the time at which the maximum concentration is reached is given by the solution of the equation

2te^{-0.25t} = 0

2e^{-0.25t} - 2te^{-0.25t} = 0

2e^{-0.25t} - 0.5te^{-0.25t} = 0

2te^{-0.25t} = 2