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Solutions to Section 1.1 True-False Review: 1. FALSE. A derivative must involve some derivative of the function y = f (x), not necessarily the first derivative. ## 2. TRUE. The initial conditions accompanying a differential equation consist of the values of y, y , . . . at t = 0. ## 3. TRUE. If we define positive velocity to be oriented downward, then where g is the acceleration due to gravity. ## 4. TRUE. We can justify this mathematically by starting from a(t) = g, and integrating twice to get v(t) = gt + c, and then s(t) = 1 2 gt 2 + ct + d, which is a quadratic equation. ## 5. FALSE. The restoring force is directed in the direction opposite to the displacement from the equilibrium position. ## 6. TRUE. According to Newton's Law of Cooling, the rate of cooling is proportional to the difference between the object's temperature and the medium's temperature. Since that difference is greater for the object at 100 • F than the object at 90 • F , the object whose temperature is 100 • F has a greater rate of cooling. ## 7. FALSE. The temperature of the object is given by T (t) = T m + ce -kt , where T m is the temperature of the medium, and c and k are constants. Since e -kt = 0, we se

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Author

Stephen W. Goode and Scott A. Annin

Language

EN

Category

nonfiction

Subjects

Mathematics, Differential Equations, Stem