Proof
Prove that if f is continuous and , then there exists a -neighborhood about (a, b) such that for every point (x, y) in the neighborhood.
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(a) Let and be continuous on the closed interval . If and , prove that there exists c between a and b such that .
(b) Show that there exists c in such that cos x = x. Use a graphing utility to approximate c to three decimal places.
Prove that if converges to and , then there exists a number such that .
Proof Prove that for any real number y there exists x in such that .