Proof (a) Let 1 (x) and 2 (x) be continuous on the closed interval [a,
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Proof
(a) Let ƒ1(x) and ƒ2(x) be continuous on the closed interval [a, b]. If ƒ1(a) < ƒ2(a) and ƒ1(b) > ƒ2(b), prove that there exists c between a and b such that ƒ1(c) = ƒ2(c).
(b) Show that there exists c in [0, π/2] such that cos x = x. Use a graphing utility to approximate c to three decimal places.
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a The proof of this result is based on the intermediate value theorem The intermediate value theo...View the full answer
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