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calc notes lecture 13

# calc notes lecture 13 - Example 3 A conical tank(with...

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Lecture Section Objectives Assignment 13 2.8 Related Rates 2.8: 1-19 odds, 23 Understanding Goals: 1. Understand relationship between variables in a function. 2. Understand how to use derivatives to solve related-rate problems. Related rates: the rates of two of more related variables that are changing with respect to time. Related rates problems : Find and solve a relation between different rates of changes. 1

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Example 1 : A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate of 1 ft/second. When the radius is 4 feet, at what rate is the total area A of the disturbed water changing? 2
Example 2 : Air is being pumped into a spherical balloon at a rate of 4.5 3 ft / min . Find the rate of change of radius when the radius is 2 feet.

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Unformatted text preview: Example 3 : A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 3 ft / min , find the rate of change of the depth of water when the water is 8 feet deep. 3 Example 4 : A tumor is modeled as being roughly spherical, with radius R. If the radius of the tumor is currently R = 0.54 cm and is increasing at the rate of 0.13 cm per month, what is the corresponding rate of change of the volume 3 4 3 R V π = ? Example 5 : A boat is pulled by a winch on a dock, and the winch is 12 feet above the deck of the boat. The winch pulls the rope at a rate of 4 feet per second. Find the speed of the boat when 13 feet of rope is out. What happens to the speed of the boat as it gets closer and closer to the dock? 4...
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calc notes lecture 13 - Example 3 A conical tank(with...

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