Calculus with Applications (11th Edition)
Calculus with Applications (11th Edition)
11th Edition
ISBN: 9780321979421
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 6.2, Problem 25E

(a)

To determine

To show: The area required that the height of the can is twice the radius and it is true for arbitrary volume V.

(b)

To determine

Whether many cans have the height twice that of radius or not.

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Chapter 6.2, Problem 24E
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Chapter 6 Solutions

Calculus with Applications (11th Edition)

Ch. 6.1 - YOUR TURN 1 Find the absolute extrema of the...Ch. 6.1 - Prob. 2YTCh. 6.1 - Prob. 1WECh. 6.1 - Prob. 2WECh. 6.1 - Prob. 1ECh. 6.1 - Find the locations of any absolute extrema for the...Ch. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6E
Ch. 6.1 - Prob. 7ECh. 6.1 - Find the locations of any absolute extrema for the...Ch. 6.1 - Prob. 9ECh. 6.1 - 10. Can a relative extremum be an absolute...Ch. 6.1 - Prob. 11ECh. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Prob. 17ECh. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Prob. 23ECh. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Prob. 25ECh. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - 43. Profit The total profit P(x) (in thousands of...Ch. 6.1 - 44. Profit A company has found that its weekly...Ch. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 53ECh. 6.1 - 54. Salmon Spawning The number of salmon swimming...Ch. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.2 - YOUR TURN 1 Find two nonnegative numbers x and y...Ch. 6.2 - EXAMPLE 2 Minimizing Time A math professor...Ch. 6.2 - Prob. 3YTCh. 6.2 - Prob. 4YTCh. 6.2 - Prob. 1WECh. 6.2 - Prob. 2WECh. 6.2 - Prob. 1ECh. 6.2 - In Exercises 1–4, use the steps shown in Exercise...Ch. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - 8. Revenue The sale of compact discs of “lesser”...Ch. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - 12. Area A farmer is constructing a rectangular...Ch. 6.2 - Prob. 13ECh. 6.2 - 14. Cost with Fixed Area A fence must be built to...Ch. 6.2 - 15. Revenue A local club is arranging a charter...Ch. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - 20. Packaging Design A company wishes to...Ch. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - 26. Container Design Your company needs to design...Ch. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - 32. Packaging Design A cylindrical box will be...Ch. 6.2 - Prob. 33ECh. 6.2 - 34. Cost Repeat Exercise 33, but make point A 7...Ch. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Maximum Sustainable Harvest In Exercises 41 and...Ch. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - 51. Postal Regulations The U.S. Postal Service...Ch. 6.3 - YOUR TURN 1 Suppose the annual demand in Example 1...Ch. 6.3 - Prob. 2YTCh. 6.3 - Prob. 3YTCh. 6.3 - Prob. 4YTCh. 6.3 - Prob. 5YTCh. 6.3 - Find the derivative of each of the following...Ch. 6.3 - Prob. 2WECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - 13. Order Quantity A bookstore has an annual...Ch. 6.3 - 14. Order Quantity A restaurant has an annual...Ch. 6.3 - Prob. 15ECh. 6.3 - 16. Lot Size A book publisher wants to know how...Ch. 6.3 - 17. Lot Size Suppose that in the inventory...Ch. 6.3 - 18. Lot Size Every year, Erin D’Aquanni sells...Ch. 6.3 - Elasticity For each of the following demand...Ch. 6.3 - Elasticity For each of the following demand...Ch. 6.3 - Elasticity For each of the following demand...Ch. 6.3 - Elasticity For each of the following demand...Ch. 6.3 - Elasticity For each of the following demand...Ch. 6.3 - Elasticity For each of the following demand...Ch. 6.3 - Elasticity Find the elasticity of demand (E) for...Ch. 6.3 - Elasticity Find the elasticity of demand (E) for...Ch. 6.3 - 27. Elasticity of Crude Oil The demand for crude...Ch. 6.3 - 28. Elasticity of Rice The demand for rice in...Ch. 6.3 - 29. Elasticity of Software The Valve Corporation,...Ch. 6.3 - 30. Elasticity The price of beef in the United...Ch. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.4 - YOUR TURN 1 Find dy/dx if x2 + y2 = xy. Ch. 6.4 - Prob. 2YTCh. 6.4 - YOUR TURN 3 The graph of y4 – x4 – y2 + x2 = 0 is...Ch. 6.4 - Prob. 4YTCh. 6.4 - Prob. 1WECh. 6.4 - Prob. 2WECh. 6.4 - Prob. 1ECh. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Prob. 5ECh. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Prob. 7ECh. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Prob. 11ECh. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Prob. 15ECh. 6.4 - Find dy/dx by implicit differentiation for the...Ch. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Find the equation of the tangent line at the given...Ch. 6.4 - Find the equation of the tangent line at the given...Ch. 6.4 - Prob. 21ECh. 6.4 - Find the equation of the tangent line at the given...Ch. 6.4 - Prob. 23ECh. 6.4 - Find the equation of the tangent line at the given...Ch. 6.4 - Find the equation of the tangent line at the given...Ch. 6.4 - Find the equation of the tangent line at the given...Ch. 6.4 - In Exercises 27–32, find the equation of the...Ch. 6.4 - In Exercises 27–32, find the equation of the...Ch. 6.4 - In Exercises 27–32, find the equation of the...Ch. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - In Exercises 27–32, find the equation of the...Ch. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - 40. Let . Find each...Ch. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 6.4 - Prob. 43ECh. 6.4 - 44. Demand The demand equation for a certain...Ch. 6.4 - Prob. 45ECh. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6.4 - Prob. 48ECh. 6.4 - Prob. 49ECh. 6.4 - Prob. 50ECh. 6.4 - Prob. 51ECh. 6.4 - Prob. 52ECh. 6.4 - Prob. 53ECh. 6.5 - Prob. 1YTCh. 6.5 - Prob. 2YTCh. 6.5 - Prob. 3YTCh. 6.5 - Prob. 4YTCh. 6.5 - Prob. 1WECh. 6.5 - Prob. 2WECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Business and Economics 9. Cost A manufacturer of...Ch. 6.5 - 10. Cost/Revenue The manufacturer in Exercise 9...Ch. 6.5 - 11. Revenue/Cost/Profit Given the revenue and cost...Ch. 6.5 - 12. Revenue/Cost/Profit Repeat Exercise 11, given...Ch. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - 18. Birds The energy cost of bird flight as a...Ch. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - 24. Distance (a) One car leaves a given point and...Ch. 6.5 - Prob. 25ECh. 6.5 - 26. Volume A spherical snowball is placed in the...Ch. 6.5 - 27. Ice Cube An ice cube that is 3 cm on each side...Ch. 6.5 - Prob. 28ECh. 6.5 - 29. Shadow Length A man 6 ft tall is walking away...Ch. 6.5 - 30. Water Level A trough has a triangular cross...Ch. 6.5 - Prob. 31ECh. 6.5 - 32. Kite Flying Christine O’Brien is flying her...Ch. 6.6 - YOUR TURN 1 Find dy if x = 8, and dx = 0.05. Ch. 6.6 - YOUR TURN 2 Approximate . Ch. 6.6 - YOUR TURN 3 Repeat Example 5 for r = 1.25 mm with...Ch. 6.6 - Prob. 1WECh. 6.6 - Prob. 2WECh. 6.6 - For Exercises 1–8, find dy for the given values of...Ch. 6.6 - For Exercises 1–8, find dy for the given values of...Ch. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Prob. 5ECh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - For Exercises 1–8, find dy for the given values of...Ch. 6.6 - Prob. 9ECh. 6.6 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.6 - Use the differential to approximate each quantity....Ch. 6.6 - Prob. 13ECh. 6.6 - Prob. 14ECh. 6.6 - Use the differential to approximate each quantity....Ch. 6.6 - Use the differential to approximate each quantity....Ch. 6.6 - Prob. 17ECh. 6.6 - Prob. 18ECh. 6.6 - Prob. 19ECh. 6.6 - Prob. 20ECh. 6.6 - Prob. 21ECh. 6.6 - Prob. 22ECh. 6.6 - Prob. 23ECh. 6.6 - Prob. 24ECh. 6.6 - Prob. 25ECh. 6.6 - Prob. 26ECh. 6.6 - Prob. 27ECh. 6.6 - Prob. 28ECh. 6.6 - Prob. 29ECh. 6.6 - Prob. 30ECh. 6.6 - Prob. 31ECh. 6.6 - Prob. 32ECh. 6.6 - Prob. 33ECh. 6.6 - Prob. 34ECh. 6.6 - Prob. 35ECh. 6.6 - Prob. 36ECh. 6.6 - Prob. 37ECh. 6.6 - Prob. 38ECh. 6.6 - 39. Measurement Error A sphere has a radius of...Ch. 6.6 - Prob. 40ECh. 6.6 - Prob. 41ECh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - 17. Find the absolute maximum and minimum of on...Ch. 6 - Prob. 18RECh. 6 - 19. When is it necessary to use implicit...Ch. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Prob. 52RECh. 6 - 53. Elasticity of Demand The demand for butter in...Ch. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 63RECh. 6 - Prob. 64RECh. 6 - Prob. 65RECh. 6 - Prob. 66RECh. 6 - Prob. 67RECh. 6 - Prob. 68RE
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