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For the following problem, you may assume as known the usual properties of the cosine function, including the fact that it is continuous. a)

 

For the following problem, you may assume as known the usual properties of the cosine function, including the fact that it is continuous. a) Show that the equation cos(x) = x has at least one real solution. b) Show that the equation x2 2 = cos(x + 1) has at least two real solutions.

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