(a) How many solutions does the equation e−x2= x have? (b) Use the intermediate value theorem to show that f(x) = e−x2− x has at least one root in the interval [0, 1]. (c) Use the Newton-Raphson method to find the approximate solution of the function f(x) = e−x2− x . Start from x0 = 0.5 and correct your answer to 4 decimal places.

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