The equation (x 0.5) e 3x = 1 has a root . a. Show, by sketching

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The equation (x − 0.5) e3x = 1 has a root α.

a. Show, by sketching the graph of y = e3x and one other suitable graph, that α is the only root of this equation.

b. Use the iterative formula xh+1= e-3xn with x1 = 0.5 to find the value of α correct to 2 decimal places. Give the value of each of  iterations to 4 decimal places.

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