Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)
2nd Edition
ISBN: 9781285101552
Author: James Stewart
Publisher: Cenage
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Textbook Question
Chapter 7.3, Problem 42E
Use cylindrical shells to find the volume of the solid.
Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height h, as shown in the figure.
(a) Guess which ring has more wood in it.
(b) Check your guess: Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h.
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Chapter 7 Solutions
Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)
Ch. 7.1 - Find the area of the shaded region.Ch. 7.1 - Prob. 2ECh. 7.1 - Find the area of the shaded region.Ch. 7.1 - Find the area of the shaded region.Ch. 7.1 - Prob. 5ECh. 7.1 - Sketch the region enclosed by the given curves....Ch. 7.1 - Prob. 7ECh. 7.1 - Sketch the region enclosed by the given curves....Ch. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - Sketch the region enclosed by the given curves and...Ch. 7.1 - 14. Sketch the region enclosed by the given curves...Ch. 7.1 - Sketch the region enclosed by the given curves and...Ch. 7.1 - Prob. 14ECh. 7.1 - Sketch the region enclosed by the given curves and...Ch. 7.1 - Sketch the region enclosed by the given curves and...Ch. 7.1 - Prob. 16ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Sketch the region enclosed by the given curves and...Ch. 7.1 - Sketch the region that lies between the curves y =...Ch. 7.1 - Graph the curves y = x2 x and y = x3 4x2 +3x on...Ch. 7.1 - Graph the region between the curves and use your...Ch. 7.1 - Graph the region between the curves and use your...Ch. 7.1 - Graph the region between the curves and use your...Ch. 7.1 - Graph the region between the curves and use your...Ch. 7.1 - Sketch the region in the xy-plane defined by the...Ch. 7.1 - Racing cars driven by Chris and Kelly are side by...Ch. 7.1 - The widths (in meters) of a kidney-shaped swimming...Ch. 7.1 - A cross-section of an airplane wing is shown....Ch. 7.1 - If the birth rate of a population is b(t) =...Ch. 7.1 - Two cars, A and B, start side by side and...Ch. 7.1 - Find a positive continuous function f such that...Ch. 7.1 - Find the area of the region bounded by the...Ch. 7.1 - Find the number b such that the line y = b divides...Ch. 7.1 - (a) Find the number a such that the line x = a...Ch. 7.1 - 59. Find the values of c such that the area of the...Ch. 7.1 - Suppose that 0 c /2. For what value of c is the...Ch. 7.1 - 61. For what values of m do the line y = mx and...Ch. 7.1 - 43. Find the area of the crescent-shaped region...Ch. 7.1 - A water storage tank has the shape of a cylinder...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 -
1–12 Find the volume of the solid obtained by...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - Find the volume of the solid obtained by rotating...Ch. 7.2 - The region enclosed by the given curves is rotated...Ch. 7.2 - The region enclosed by the given curves is rotated...Ch. 7.2 - The region enclosed by the given curves is rotated...Ch. 7.2 - The region enclosed by the given curves is rotated...Ch. 7.2 - The region enclosed by the given curves is rotated...Ch. 7.2 - The region enclosed by the given curves is rotated...Ch. 7.2 - Set up an integral for the volume of the solid...Ch. 7.2 - Set up an integral for the volume of the solid...Ch. 7.2 - Set up an integral for the volume of the solid...Ch. 7.2 - Set up an integral for the volume of the solid...Ch. 7.2 - Use a graph to find approximate x-coordinates of...Ch. 7.2 - Use a graph to find approximate x-coordinates of...Ch. 7.2 - Each integral represents the volume of a solid....Ch. 7.2 - Each integral represents the volume of a solid....Ch. 7.2 - A CAT scan produces equally spaced cross-sectional...Ch. 7.2 - A log 10 m long is cut at 1-meter intervals and...Ch. 7.2 - 47. Find the volume of the described solid S.
A...Ch. 7.2 - Find the volume of the described solid S. A...Ch. 7.2 - Find the volume of the described solid S. A cap of...Ch. 7.2 - Find the volume of the described solid S. A...Ch. 7.2 - Find the volume of the described solid S. A...Ch. 7.2 - Find the volume of the described solid S. A...Ch. 7.2 - Find the volume of the described solid S. A...Ch. 7.2 - 54. Find the volume of the described solid S.
The...Ch. 7.2 - Find the volume of the described solid S. The base...Ch. 7.2 - Find the volume of the described solid S. The base...Ch. 7.2 - Find the volume of the described solid S. The base...Ch. 7.2 - Find the volume of the described solid S. The base...Ch. 7.2 - The base of S is the same base as in Exercise 42,...Ch. 7.2 - The base of S is a circular disk with radius r....Ch. 7.2 - (a) Set up an integral for the volume of a solid...Ch. 7.2 - A wedge is cut out of a circular cylinder of...Ch. 7.2 - (a) Cavalieris Principle states that if a family...Ch. 7.2 - Find the volume common to two circular cylinders,...Ch. 7.2 - Prob. 51ECh. 7.2 - A bowl is shaped like a hemisphere with diameter...Ch. 7.2 - A hole of radius r is bored through the middle of...Ch. 7.2 - A hole of radius r is bored through the center of...Ch. 7.2 - Some of the pioneers of calculus, such as Kepler...Ch. 7.3 - Let S be the solid obtained by rotating the region...Ch. 7.3 - Let S be the solid obtained by rotating the region...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Let V be the volume of the solid obtained by...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Prob. 14ECh. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - 17. Use the method of cylindrical shells to find...Ch. 7.3 - Use the method of cylindrical shells to find the...Ch. 7.3 - 15-20 Use the method of cylindrical shells to find...Ch. 7.3 - 15-20 Use the method of cylindrical shells to find...Ch. 7.3 - (a) Set up an integral for the volume of the solid...Ch. 7.3 - (a) Set up an integral for the volume of the solid...Ch. 7.3 - (a) Set up an integral for the volume of the solid...Ch. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Use the Midpoint Rule with n = 4 to estimate the...Ch. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - 39-41 Use cylindrical shells to find the volume of...Ch. 7.3 - Use cylindrical shells to find the volume of the...Ch. 7.3 - Use cylindrical shells to find the volume of the...Ch. 7.3 - Prob. 43ECh. 7.4 - Use the arc length formula (3) to find the length...Ch. 7.4 - Use the arc length formula to find the length of...Ch. 7.4 - Set up an integral that represents the length of...Ch. 7.4 - Prob. 4ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Find the exact length of the curve. 15. y = ln(sec...Ch. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Graph the curve and visually estimate its length....Ch. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Use Simpsons Rule with n = 10 to estimate the arc...Ch. 7.4 - Prob. 25ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Find the arc length function for the curve...Ch. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 35ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 36ECh. 7.5 - 41550-8.2-1E
1–6. (a) Set up an integral for the...Ch. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - 5-12 Find the exact area of the surface obtained...Ch. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Find the exact area of the surface obtained by...Ch. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - The given curve is rotated about the y-axis. Find...Ch. 7.5 - Prob. 19ECh. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - Prob. 23ECh. 7.5 - Prob. 24ECh. 7.5 - Prob. 25ECh. 7.5 - Prob. 26ECh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Shown is the graph of a force function (in...Ch. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - A spring has a natural length of 20 cm. If a 25-N...Ch. 7.6 - Suppose that 2 J of work is needed to stretch a...Ch. 7.6 - If 6 J of work is needed to stretch a spring from...Ch. 7.6 - Prob. 9ECh. 7.6 - Show how to approximate the required work by a...Ch. 7.6 - Prob. 10ECh. 7.6 - Show how to approximate the required work by a...Ch. 7.6 - Show how to approximate the required work by a...Ch. 7.6 - Show how to approximate the required work by a...Ch. 7.6 - Show how to approximate the required work by a...Ch. 7.6 - 21. Show how to approximate the required work by a...Ch. 7.6 - The tank shown is full of water.
Find the work...Ch. 7.6 - (a) The tank shown is full of water. Given that...Ch. 7.6 - 29. When gas expands in a cylinder with radius r,...Ch. 7.6 - Prob. 20ECh. 7.6 - 33. (a) Newton’s Law of Gravitation states that...Ch. 7.6 - The Great Pyramid of King Khufu was built of...Ch. 7.6 - Use an improper integral and information from...Ch. 7.6 - Find the escape velocity v0 that is needed to...Ch. 7.6 - 2529 A vertical plate is submerged (or partially...Ch. 7.6 - 2529 A vertical plate is submerged (or partially...Ch. 7.6 - A vertical plate is submerged (or partially...Ch. 7.6 - 2529 A vertical plate is submerged (or partially...Ch. 7.6 - A vertical plate is submerged (or partially...Ch. 7.6 - A milk truck carries milk with density 64.6 lb/ft3...Ch. 7.6 - A trough is filled with a liquid of density 840...Ch. 7.6 - A vertical dam has a semicircular gate as shown in...Ch. 7.6 - Prob. 32ECh. 7.6 - A swimming pool is 20 ft wide and 40 ft long and...Ch. 7.6 - A metal plate was found submerged vertically in...Ch. 7.6 - Point-masses mi arc located on the x-axis as...Ch. 7.6 - The masses mi, are located at the points Pi. Find...Ch. 7.6 - 41550-8.3-24E
23–24 The masses mi, are located at...Ch. 7.6 - Sketch the region bounded by the curves, and...Ch. 7.6 - Sketch the region bounded by the curves, and...Ch. 7.6 - Sketch the region bounded by the curves, and...Ch. 7.6 - Sketch the region bounded by the curves, and...Ch. 7.6 - Find the centroid of the region bounded by the...Ch. 7.6 - Find the centroid of the region bounded by the...Ch. 7.6 - Find the centroid of the region bounded by the...Ch. 7.6 - Find the centroid of the region bounded by the...Ch. 7.6 - 4748 Calculate the moments Mx and My and the...Ch. 7.6 - 4748 Calculate the moments Mx and My and the...Ch. 7.6 - Prove that the centroid of any triangle is located...Ch. 7.6 - Find the centroid of the region shown, not by...Ch. 7.6 - Find the centroid of the region shown, not by...Ch. 7.6 - Use the Theorem of Pappus to find the volume of...Ch. 7.6 - Use the Theorem of Pappus to find the volume of...Ch. 7.6 - Use the Theorem of Pappus to find the volume of...Ch. 7.6 - 41550-8.3-50E
50. Let ℛ be the region that lies...Ch. 7.6 - Prove Formulas 13. 13....Ch. 7.7 - Psychologists interested in learning theory study...Ch. 7.7 - Prob. 21ECh. 7.7 - Match the differential equation with its direction...Ch. 7.7 - Prob. 23ECh. 7.7 - Match the differential equation with its direction...Ch. 7.7 - Prob. 25ECh. 7.7 - Prob. 26ECh. 7.7 - 41550-9.2-9E
9–10 Sketch a direction field for the...Ch. 7.7 - Sketch a direction field for the differential...Ch. 7.7 - Sketch the direction field of the differential...Ch. 7.7 - Sketch the direction field of the differential...Ch. 7.7 - Sketch the direction field of the differential...Ch. 7.7 - Sketch the direction field of the differential...Ch. 7.7 - Prob. 1ECh. 7.7 - Prob. 2ECh. 7.7 - Solve the differential equation. 3. xyy=x2+1Ch. 7.7 - Solve the differential equation. (y2 + xy2)y = 1Ch. 7.7 - Solve the differential equation. (y + sin y)y = x...Ch. 7.7 - Solve the differential equation. dyd=eysin2ysecCh. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - Find the solution of the differential equation...Ch. 7.7 - Prob. 10ECh. 7.7 - Prob. 11ECh. 7.7 - Find the solution of the differential equation...Ch. 7.7 - Prob. 13ECh. 7.7 - Prob. 14ECh. 7.7 - Prob. 15ECh. 7.7 - Prob. 16ECh. 7.7 - Prob. 17ECh. 7.7 - Prob. 18ECh. 7.7 - A sphere with radius 1 m has temperature 15C. It...Ch. 7.7 - A glucose solution is administered intravenously...Ch. 7.7 - A certain small country has 10 billion in paper...Ch. 7.7 - Write the solution of the logistic initial-value...Ch. 7.7 - A tank contains 1000 L of brine with 15 kg of...Ch. 7.7 - The air in a room with volume 180 m3 contains...Ch. 7.7 - A vat with 500 gallons of beer contains 4% alcohol...Ch. 7.7 - A tank contains 1000 L of pure water. Brine that...Ch. 7.7 - When a raindrop falls, it increases in size and so...Ch. 7.7 - 41550-9.3-50E
50. An object of mass m is moving...Ch. 7.7 - According to Newtons Law of Universal Gravitation,...Ch. 7.7 - The Pacific halibut fishery has been modeled by...Ch. 7.7 - One model for the spread of a rumor is that the...Ch. 7.7 - 41550-9.4-12E
12. Biologists stocked a lake with...Ch. 7.7 - (a) Show that if y satisfies the logistic equation...Ch. 7.7 - For a fixed value of M (say M = 10), the family of...Ch. 7 - Prob. 1RCCCh. 7 - Suppose that Sue runs faster than Kathy throughout...Ch. 7 - 3. (a) Suppose S is a solid with known...Ch. 7 - (a) What is the volume of a cylindrical shell? (b)...Ch. 7 - Suppose that you push a book across a 6-meter-long...Ch. 7 - 1. Find the area of the region bounded by the...Ch. 7 - Prob. 2RECh. 7 - Prob. 4RECh. 7 - Prob. 3RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - A force of 30 N is required to maintain a spring...Ch. 7 - A 1600-lb elevator is suspended by a 200-ft cable...Ch. 7 - 29. A tank full of water has the shape of a...Ch. 7 - Let 1, be the region bounded by y = x2, y = 0, and...Ch. 7 - Prob. 5RCCCh. 7 - Prob. 6RCCCh. 7 - Prob. 8RCCCh. 7 - Prob. 9RCCCh. 7 - Prob. 10RCCCh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Use Simpson's Rule with n = 10 to estimate the...Ch. 7 - Use Simpsons Rule with n = 10 to estimate the area...Ch. 7 - Find the length of the curve y=1xt1dt1x16Ch. 7 - Prob. 32RECh. 7 - A gate in an irrigation canal is constructed in...Ch. 7 - A trough is filled with water and its vertical...Ch. 7 - Find the centroid of the region shown.Ch. 7 - Find the centroid of the region bounded by the...Ch. 7 - Find the centroid of the region bounded by the...Ch. 7 - Find the volume obtained when the circle of radius...Ch. 7 - 41550-8-18RE
18. Use the Theorem of Pappus and the...Ch. 7 - Prob. 11RCCCh. 7 - Prob. 12RCCCh. 7 - Prob. 13RCCCh. 7 - (a) Sketch a direction field for the differential...Ch. 7 - Prob. 44RECh. 7 - Solve the differential equation. 7. 2yey2y=2x+3xCh. 7 - Solve the initial-value problem. 9....Ch. 7 - 41550-9-10RE
9–11. Solve the initial-value...
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