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Unformatted text preview: f ( t ) =16 t 2 + 1600 ±ind the time at which the ball hits the ground. Graph h = f ( t ): Lecture 9 11 Note: f ( t ) is continuous over the interval and height h ranges from Now consider h = 1200. Find t so that f ( t ) = 1200. Lecture 9 12 The Intermediate Value Theorem If f is a continuous function on a closed interval [ a, b ], and if M is a number between f ( a ) and f ( b ), then Lecture 9 13 There is an important consequence of the Intermediate Value Theorem: Theorem If f is continuous on [ a, b ], and if f ( a ) and f ( b ) have opposite signs, there is at least one solution of the equation f ( x ) = 0 in the interval ( a, b ). Lecture 9 14 ex. Show that the function f ( x ) = x 25 x + 2 must have a zero in the interval (1 , 3). What about f ( x ) = x 25 x + 2 x 2 ?...
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 Spring '08
 Smith
 Calculus, Topology, Continuity, Continuous function

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