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Unformatted text preview: ) at the point ( x , y ) intersect the x-axis? 8. The volume of a spherical balloon is decreasing at the instantaneous rate of − 10 cm 3 /sec, at the moment when its radius is 20 cm. At that moment, how rapidly is its radius decreasing? 9. Where are the following functions discontinuous? 1 + x 2 d a ) sec x b ) c ) x 1 − x 2 dx | | 10. A radioactive substance decays according to a law A = A e − rt , where A ( t ) is the amount in present at time t , and r is a positive constant. a) Derive an expression in terms of r for the time it takes for the amount to fall to one-quarter of the initial amount A . b) At the moment when the amount has fallen to 1/4 the initial amount, how rapidly is the amount falling? (Units: grams, seconds.)...
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