Proof (a) Let 1 (x) and 2 (x) be continuous on the closed interval a, b If 1 (a) 2 (a) and 1 (b) 2 (b), prove that there exists c between a and b such that 1 (c) 2 (c) (b) Show that there exists c in 0, 2 such that cos x x Use a graphing utility to approximate c to three decimal places

Question: Proof (a) Let 1 (x) and 2 (x) be continuous on the closed interval [a, b]. If 1 (a) < 2

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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