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ton's method proble

ton's method proble

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Decide if each of the following problems is a linearization problem, an optimization prob-lem, a related rates problem, a graphing problem, or a Newton's method problem then do the steps it says.

Decide if each of the following problems is a linearization problem, an optimization prob- lem, a related rates problem, a graphing problem, or a Newton's method problem. Identify. Label the problem as one of the five types or explain that it is not exactly one of those types (and how you know). Begin solution. For each problem, start the solution. Linearization. State what function you would linearize and where you would linearize it. Optimization. Draw a diagram to define your variables. Write the function you would optimize, including the domain of the function. Related Rates. Draw a diagram to define your variables. Write an equation that relates your variables. Graphing. State the function, its domain, and any critical points in the domain. Newton's method. State the function to which you would apply Newton's method, your initial point, and the Newton iteration. Other. Explain how you might use calculus to solve this problem.
Transcribed Image Text:Decide if each of the following problems is a linearization problem, an optimization prob- lem, a related rates problem, a graphing problem, or a Newton's method problem. Identify. Label the problem as one of the five types or explain that it is not exactly one of those types (and how you know). Begin solution. For each problem, start the solution. Linearization. State what function you would linearize and where you would linearize it. Optimization. Draw a diagram to define your variables. Write the function you would optimize, including the domain of the function. Related Rates. Draw a diagram to define your variables. Write an equation that relates your variables. Graphing. State the function, its domain, and any critical points in the domain. Newton's method. State the function to which you would apply Newton's method, your initial point, and the Newton iteration. Other. Explain how you might use calculus to solve this problem.
4. When you study, you add knowledge to your mind, but the rate at which it accumulates varies according to the conditions – in fact, some conditions can make this accumulation rate negative! Here's what happens when you study all night: the rate of knowledge accumulation at time t (measured in hours after 9: 00 PM) is given by the formula j(t) = 2 -t+ 2 nuggets/hour (nuggets of wisdom is the standard unit for knowledge). At what time are you accu- mulating knowledge at the greatest rate? 5. A rectangular storage container with an open top is to have a volume of 32 cubic meters. The length of its base is twice the width. Material for the base costs 2 dollars per square meter. Material for the sides costs 1.50 dollars per square meter. Find the cost of materials for the cheapest such container. 1 6. Gravel is being dumped from a conveyor belt at a rate of 8 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 20 feet high?
Transcribed Image Text:4. When you study, you add knowledge to your mind, but the rate at which it accumulates varies according to the conditions – in fact, some conditions can make this accumulation rate negative! Here's what happens when you study all night: the rate of knowledge accumulation at time t (measured in hours after 9: 00 PM) is given by the formula j(t) = 2 -t+ 2 nuggets/hour (nuggets of wisdom is the standard unit for knowledge). At what time are you accu- mulating knowledge at the greatest rate? 5. A rectangular storage container with an open top is to have a volume of 32 cubic meters. The length of its base is twice the width. Material for the base costs 2 dollars per square meter. Material for the sides costs 1.50 dollars per square meter. Find the cost of materials for the cheapest such container. 1 6. Gravel is being dumped from a conveyor belt at a rate of 8 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 20 feet high?
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