Question 2 Suppose that F is a function that is continuous at all points in the...

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Question 2 Suppose that F is a function that is continuous at all points in the interval [0, 1]. Suppose also that for all b < 1 there is some x such that 0 x 1 and sin(F(x)) > b. Prove that there is some point z in the interval [0, 1] such that sin(F(2)) = 1. Your proof must quote all relevant theorems from the text and show that their hypotheses are satisfied. Question 2 Suppose that F is a function that is continuous at all points in the interval [0, 1]. Suppose also that for all b < 1 there is some x such that 0 x 1 and sin(F(x)) > b. Prove that there is some point z in the interval [0, 1] such that sin(F(2)) = 1. Your proof must quote all relevant theorems from the text and show that their hypotheses are satisfied.