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Section 1.3 - Methods and Techniques

Suppose we have a situation that's changing over time, e.g. a cone that's filling up with water. The cone has two variables, the height of the liquid and its volume, that are both changing with respect to time. "Related rates" refers to a method for finding a relationship between the rates at which each of those variables is changing.


We usually think of formulas as static things - you put in numbers and you get out a number. Instead, suppose we think about each variable as being something that changes over time. For example, as a ripple spreads through a pond, both the radius and the area are changing but at different rates. In this lecture, we're going to look at a way that uses the idea of implicit differentiation to find relationships between those rates of change.
Now that we've got the concept or related rates down, we can talk about how this can be applied to specific real world situations.

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