UFCalcSet5 - Exercises UF Calculus Set 5 1. Determine...

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Exercises UF Calculus Set 5 1. Determine whether the following represent one-to-one functions: (a) a rule that associates a person with his/her nuclear DNA (b) a rule that associates a person with his/her current set of fingerprints (c) a rule that associates, to a given time, the distance from a swinging pendulum to its lowest point (d) a rule that associates, to a given distance traveled, the speed of an object falling from a building without air resistence 2. The function f ( x ) = x + e x - 1 is one-to-one. By inspection, what is f - 1 (0) ? what is f - 1 ( e ) ? 3. A tank continuously drains so that the volume V of water (in gallons) remaining in the tank after t minutes is V ( t ) = 100(1 - t 20 ) 2 . (a) What is the domain of V ( t ) by the context of the problem? What is the range? (b) What is implied about the physical nature of the problem that ensures V ( t ) is one-to-one on its domain? Find the inverse function. (c) What is
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UFCalcSet5 - Exercises UF Calculus Set 5 1. Determine...

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