Starting from the interval (0.4, 0.99], conduct JUST THREE iterations of the Bin

Question

Starting from the interval (0.4, 0.99], conduct JUST THREE iterations of the Binary Search algorithm (method) that is used here to solve the equation as follows: x^2e^2x - 1 = 0. It is NOT required to Solve the above equation for x in full. Just conduct three iterations of the method and provide your result for the midpoint of the interval that the corresponds to the iteration number 3. The numerical value of the midpoint of the interval that you have just found must be rounded-off to four significant decimal digits and presented below:_____________(your numerical result for the midpoint must be written here)

Explanation / Answer

f(x)= x2 e2x -1

f(0.4) = -0.5332 and f(0.99) =6.09

Iteration 0 Midpoint 0.7 , f(0.7)= 0.987

Iteration 1: Midpoint ( mid point of 0.4 and 0.7) =0.55) , f(0.55) = -0.091

Iteration 2: Midpoint (midpoint of ).55 and 0.7) =0.625   f(0.625) = 0.3634

Iteration 3: Midpoint (midpoit of 0.55 and 0.625) =0.5875, f(0.5875) =0. 117665275459

                                                                                                          = 0.1177 (rounding off to four decimal places)

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