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Unformatted text preview: x is y increasing? For which values of x is y decreasing? c) (6 points) Calculate lim x → + x x . (over) c ± by Cornell University. All rights reserved 4) The temperature H of a ﬂuid in degrees Centigrade at time t minutes is given by the function H ( t ) = ± 1 π tan-1 ( t ) + t 1 + t ² 100 ◦ C on the domain t ≥ 0. So H (1) = 75 ◦ C . a) (7 points) Show that H ( t ) is a one-to-one function. b) (7 points) Calculate ( H-1 ) (75 ◦ C ). 5) The size of a population y ( t ) evolves according to the diﬀerential equation dy dt =-2 y, y (0) = y . a) (6 points) Write an expression for y ( t ). b) (6 points) What happens to the size of the population as t → ∞ ? Does your answer depend on the initial size y ? c) (6 points) How long does it take for the size of the population to become a quarter of its starting size? Does your answer depend on the initial size y ?...
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- Fall '07
- Math, Inverse function