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Chapter 6: Q. 5 (page 573)
Fill in the blanks to complete each of the following theorem statements.
If an object with temperature is in a location with constant ambient temperature , then the temperature of the object can be modeled by a differential equation of the form , with solution .
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Consider the region between the graph of and the x-axis on [2,5]. For each line of rotation given in Exercises 35– 40, use definite integrals to find the volume of the resulting solid.
Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.
find an equation that gives y as an implicit function of x. Then draw the continuous curve that satisfies this differential equation and passes through the point (2, 0).
In the process of solving by separation of variables, we obtain the equation . After solving for , this equation becomes . How is related to ? What happened to the absolute value?
Each of the definite integrals in Exercises 19–24 represents the volume of a solid of revolution obtained by rotating a region around either the x- or y-axis. Find this region.
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