Question: 12. Use the Intermediate Value Theorem to show there is at least one real solution for the equation 2 sin x = 1 + 3

12. Use the Intermediate Value Theorem to show there is at least one real solution for the equation 2 sin x = 1 + 3 cos x 13. Use the Intermediate Value Theorem to show there is at least one real solution for the equation 2vx + 3 = ex (Assume we know f(x) = ex is continuous everywhere.) 14 . Use the Intermediate Value Theorem to prove there exists a real number c such that c2 = 3. 15. Suppose fis continuous on [1, 5] and the only solutions of the equation f (x) = 6 are x = 1 and x = 4. If f (2) = 8, explain why f (3) > 6

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