微积分I（标准路径） · free preview
§3.1 Related rates
如果两个相互关联的量（例如球形气球的半径和体积）都在作为时间的隐函数而变化，那么它们的变化率之间有什么关系？也就是说，这些量取值之间的关系如何影响它们各自对时间的导数之间的关系？
1. Introduction
Introduction
2. A spherical balloon …
A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when or when ? Why?
Draw at least three different spheres with different radii. As the volume changes, what other aspects of the balloon also change?
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