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Unformatted text preview: Lecture 16 — Related Rates Recall our problem of a ladder sliding away from a wall. Examine the pictures below. If we freeze the picture at a particular time t , then the values of x and y can be measured and recorded; therefore x and y are both functions of time t , say x ( t ) and y ( t ) . By Pythagorean Theorem, we have the following identity for all t during which the ladder is in motion: and hence by chain rule, We did this without having to find formulas for x ( t ) and y ( t ) ...knowing that those functions satisfied an identity allowed us to find a relationship between their rates of change dy dt and dx dt . Suppose, in our ladder problem, that we know the ladder is sliding out from the wall at a constant 2 m/s. At what rate is y changing when the ladder is 6 feet from the wall? 8 feet from the wall? Suppose the ladder does not slide out at a constant rate, but we use a device to measure that it is sliding out at 2 m/s at the instant it is 6 feet from the wall....
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 Spring '08
 ALL
 Calculus, Derivative, Pythagorean Theorem, Cape Canaveral

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