Unformatted text preview: 2 ] such that cos c2 c = 0. (5 points). Let f ( x ) = cos x2 x . Note that f is continuous since it is the diﬀerence of two continuous functions. Further, note that f (0) = 10 = 1 > 0 and f ( π 2 ) = 0π =π < 0. Thus, by the intermediate value theorem, there exists a c ∈ [0 , π 2 ] such that f ( c ) = 0, which is to say that cos c2 c = 0....
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 Summer '08
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 Math, Calculus, Intermediate Value Theorem, lim, Continuous function

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