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Numerical Methods

Bisection

         

The equation \(\displaystyle e^x = \frac{1}{x}\) has a root between \(0\) and \(1.\) If we apply the bisecton method 4 times, which of the following intervals will we end up with?

One of the roots of the equation \(\displaystyle f(x)=3x+\sin x-e^x = 0\) lies between \(0\) and \(0.5.\) If we apply the bisecton method 5 times, which of the following intervals will we end up with?

Determine the value of \(\displaystyle \sqrt[3]{5}\) by using the bisecton method. Let the width of the final interval less than \(0.02,\) and start with the interval \([1,2].\) Then, guess the upper boundary of the final interval as the value of \(\displaystyle \sqrt[3]{5}.\)

The equation \(\displaystyle (x-2)^3+(x-2)^2-1=0\) has a root between \(2\) and \(3.\) If we apply the bisecton method 6 times, which of the following intervals will we end up with?

The equation \(\displaystyle 2^x+2^{-x} = 3\) has a root between \(1\) and \(2.\) If we apply the bisecton method 5 times, which of the following intervals will we end up with?

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