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lecture20 - Lecture 20 Related Rates(Chapter 3 Section 20...

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Lecture 20: Related Rates (Chapter 3, Section 20) Consider the following example: A point is moving along the graph of the function y = 1 1 + x 2 so that the velocity in the x direction as it passes the point ( ¡ 2 ; 1 5 ) is 2 cm/min. What is the velocity in the y direction at this time?
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2 Related Rates allows us to flnd the rate of change of one quantity in terms of the rate of change of a related quantity. To solve a related rates problem: 1) Identify the desired rate of change; assign variables to all related quantities. Determine what rate(s) and information are given. Draw a sketch if possible. 2) Write an equation (mathematical model ) relating the variables involved. 3) Difierentiate the equation implicitly with respect to time. 4) Substitute known values and solve for the desired rate of change.
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3 ex. A spherical balloon is in ated with gas at a rate of 8 cubic ft/min. How fast is the radius changing when the volume is 36 cubic ft?
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