we want to show that equation x^2 = exp(x) for x R_0 = [0; +) has a unique solution x_0 and want to determine a rational approximation for x_0. To do this, we proceed as follows:

a) We consider the function f : R_0 R, x x^2 exp(x). Show that f is continuously and strictly increasing, and calculate f(0) and f(1)

b )Using the bisection method, determine q Q with |q x0| < 0,