Question: Consider the equation x 5 + 7x - 4 = 0. (1) Show that the equation has a unique root in the interval [0; 1].

Consider the equation x⁵ + 7x - 4 = 0. (1) Show that the equation has a unique root in the interval [0; 1]. (2) Rewrite the equation in the form x = g(x) for some continuous function g. (3) Use a Theoreme to show that the iteration sequence x_n+1 = g(xn) converges for any initial value in the range [0; 1]. (4) Use the x-point method to estimate the value of the root of the equation x⁵+7x-4 = 0 in the interval [0; 1] correct to to 4 decimal places. Start with x₀ = 0:

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