Calculus of a Single Variable
Calculus of a Single Variable
11th Edition
ISBN: 9781337275361
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Concept explainers

Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 7.1, Problem 68E

(a)

To determine

What does the area between the two given curves represent provided that astate legislature is debating for two proposals for eliminating the annual budget deficits after 10 years and the rate of decrease of the deficits for each proposal is

Calculus of a Single Variable, Chapter 7.1, Problem 68E , additional homework tip 1

(b)

To determine

Which proposal is better for minimizing the cumulative state deficit provided that a state legislature is debating for two proposals for eliminating the annual budget deficits after 10 years and the rate of decrease of the deficits for each proposal is

Calculus of a Single Variable, Chapter 7.1, Problem 68E , additional homework tip 2

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(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.
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(14 points) Let f: R3 R and T: R3. →R³ be defined by f(x, y, z) = ln(x²+ y²+2²), T(p, 0,4)=(psin cos 0, psin sin, pcos). (a) (4 points) Write out the composition g(p, 0, 4) = (foT)(p,, ) explicitly. Then calculate the gradient Vg directly, i.e. without using the chain rule. (b) (4 points) Calculate the gradient Vf(x, y, z) where (x, y, z) = T(p, 0,4). (c) (6 points) Calculate the derivative matrix DT(p, 0, p). Then use the Chain Rule to calculate Vg(r,0,4).

Chapter 7 Solutions

Calculus of a Single Variable

Ch. 7.1 - CONCEPT CHECK Area What is the geometric...Ch. 7.1 - Prob. 2ECh. 7.1 - CONCEPT CHECK Area Between Intersecting Curves...Ch. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Writing a Definite Integral In Exercises 5-10,...Ch. 7.1 - Prob. 7ECh. 7.1 - Writing a Definite Integral In Exercises 5-10,...Ch. 7.1 - Writing a Definite Integral In Exercises 510,...Ch. 7.1 - Writing a Definite Integral In Exercises 5-10,...
Ch. 7.1 - Finding a Region In Exercises 11-14, the integrand...Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Finding a Region In Exercises 1114, the integrand...Ch. 7.1 - Prob. 15ECh. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Prob. 25ECh. 7.1 - Finding the Area of a Region In Exercises 15-28,...Ch. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Comparing Methods In Exercises 29 and 30, find the...Ch. 7.1 - Comparing Methods In Exercises 29 and 30, find the...Ch. 7.1 - Finding the Area of a Region In Exercises 31-36,...Ch. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Finding the Area of a Region In Exercises 31-36,...Ch. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Finding the Area of a Region In Exercises 47-50,...Ch. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Finding the Area of a Region Find the area of the...Ch. 7.1 - Integration as an Accumulation Process In...Ch. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - Prob. 65ECh. 7.1 - Prob. 66ECh. 7.1 - EXPLORING CONCEPTS Interpreting Integrals Two cars...Ch. 7.1 - Prob. 68ECh. 7.1 - Dividing a Region In Exercises 69 and 70, find b...Ch. 7.1 - Prob. 70ECh. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Limits and Integrals In Exercises 73 and 74,...Ch. 7.1 - Prob. 75ECh. 7.1 - Prob. 76ECh. 7.1 - Lorenz Curve Economists use Lorenz curves to...Ch. 7.1 - Profit The chief financial officer of a company...Ch. 7.1 - Building Design Concrete sections for a new...Ch. 7.1 - Mechanical Design The surface of a machine part is...Ch. 7.1 - Prob. 81ECh. 7.1 - Prob. 82ECh. 7.1 - Prob. 83ECh. 7.1 - Prob. 84ECh. 7.1 - True or False? In Exercises 83-86, determine...Ch. 7.1 - Prob. 86ECh. 7.1 - The horizontal line y=c intersects the curve...Ch. 7.2 - CONCEPT CHECK Disk Method Explain how to use the...Ch. 7.2 - CONCEPT CHECK Comparing Methods What is the...Ch. 7.2 - CONCEPT CHECK Finding the Volume of a Solid In...Ch. 7.2 - CONCEPT CHECK Finding the Volume of a Solid...Ch. 7.2 - Finding the Volume of a Solid In Exercises 58,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 58,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 58,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 5-8,...Ch. 7.2 - Prob. 9ECh. 7.2 - Finding the Volume of a Solid In Exercises 912,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 912,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 912,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 13-16,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 13-16,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 13-16,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 13-16,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 1720,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 17-20,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 17-20,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 17-20,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 21-24,...Ch. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Finding the Volume of a Solid In Exercises 21-24,...Ch. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Prob. 30ECh. 7.2 - Finding the Volume of a Solid In Exercises 25-32,...Ch. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Finding the Volume of a Solid In Exercises 4148,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Prob. 43ECh. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Finding the Volume of a Solid In Exercises 41-48,...Ch. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.2 - Finding the Volume of a Solid Using Technology In...Ch. 7.2 - Prob. 57ECh. 7.2 - Dividing a SolidIn Exercises 57 and 58, consider...Ch. 7.2 - Prob. 60ECh. 7.2 - Prob. 65ECh. 7.2 - Volume of a Container A container can be modeled...Ch. 7.2 - Finding Volumes of Solids Find the volumes of the...Ch. 7.2 - Minimum Volume The function y=4(x2/4) on the...Ch. 7.2 - Prob. 70ECh. 7.2 - Cavalieris Theorem Prove that if two solids have...Ch. 7.3 - CONCEPT CHECK Shell Method Explain how to use the...Ch. 7.3 - Prob. 2ECh. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 3-12,...Ch. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Prob. 19ECh. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 13-22,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 23-26,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 23-26,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 23-26,...Ch. 7.3 - Finding the Volume of a Solid In Exercises 23-26,...Ch. 7.3 - Prob. 27ECh. 7.3 - Choosing a Method In Exercises 27 and 28, decide...Ch. 7.3 - Choosing a Method In Exercises 29-32, use the disk...Ch. 7.3 - Prob. 30ECh. 7.3 - Choosing a Method In Exercises 29-32, use the disk...Ch. 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 - Prob. 40ECh. 7.3 - Comparing Volumes The region in the figure is...Ch. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Machine Part A solid is generated by revolving the...Ch. 7.3 - Prob. 48ECh. 7.3 - Volume of a Torus A torus is formed by revolving...Ch. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Finding Volumes of Solids Consider the graph of...Ch. 7.4 - CONCEPT CHECK Rectifiable Curve Describe the...Ch. 7.4 - CONCEPT CHECK Arc Length Explain how to find the...Ch. 7.4 - CONCEPT CHECK Arc Length Name a function for which...Ch. 7.4 - CONCEPT CHECK Surface of Revolution Describe a...Ch. 7.4 - Finding Distance Using Two Methods In Exercises 5...Ch. 7.4 - Finding Distance Using Two Methods In Exercises 5...Ch. 7.4 - Prob. 7ECh. 7.4 - Finding Arc Length In Exercises 720, find the arc...Ch. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Prob. 12ECh. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Prob. 14ECh. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Finding Arc Length In Exercises 7-20, find the arc...Ch. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Finding Arc Length In Exercises 21-30, (a) sketch...Ch. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Length of a Cable An electric cable is hung...Ch. 7.4 - Roof Area A barn is 100 feet long and 40 feet wide...Ch. 7.4 - Length of Gateway Arch The Gateway Arch in St....Ch. 7.4 - Astroid Find the total length of the graph of the...Ch. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Finding the Area of a Surface of Revolution In...Ch. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Verifying a Formula (a) Given a circular sector...Ch. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Modeling Data Property bounded by two...Ch. 7.4 - Prob. 63ECh. 7.4 - Prob. 64ECh. 7.4 - Prob. 65ECh. 7.4 - Approximating Arc Length or Surface Area In...Ch. 7.4 - Prob. 67ECh. 7.4 - Approximating Arc Length or Surface Area In...Ch. 7.4 - Suspension Bridge A cable for a suspension bridge...Ch. 7.4 - Suspension Bridge The Humber Bridge, located in...Ch. 7.4 - Arc Length and Area Let C be the curve given by...Ch. 7.4 - PUTNAM EXAM CHALLENGE Find the length of the curve...Ch. 7.5 - CONCEPT CHECK Work How do you know when work is...Ch. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Constant Force In Exercises 5-8, determine the...Ch. 7.5 - Prob. 9ECh. 7.5 - Hooke's Law In Exercises 9-14, use Hookes Law to...Ch. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Hooke's Law In Exercises �-14, use Hookes Law to...Ch. 7.5 - Propulsion Neglecting air resistance and the...Ch. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.5 - Pumping Water A rectangular tank with a base 4...Ch. 7.5 - Think About It Explain why the answer in part (b)...Ch. 7.5 - Pumping Water A cylindrical water tank 4 meters...Ch. 7.5 - Prob. 22ECh. 7.5 - Prob. 23ECh. 7.5 - Pumping Water Water is pumped in through the...Ch. 7.5 - Pumping Water A hemispherical tank of radius 6...Ch. 7.5 - Prob. 26ECh. 7.5 - Pumping Gasoline In Exercises 27 and 28, find the...Ch. 7.5 - Pumping Gasoline In Exercises 27 and 28, find the...Ch. 7.5 - Prob. 29ECh. 7.5 - Prob. 30ECh. 7.5 - Prob. 31ECh. 7.5 - Winding a Chain In Exercises 29-32, consider a...Ch. 7.5 - Prob. 33ECh. 7.5 - Prob. 34ECh. 7.5 - Prob. 35ECh. 7.5 - Prob. 36ECh. 7.5 - Prob. 37ECh. 7.5 - Prob. 38ECh. 7.5 - Electric Force Two electrons repel each other with...Ch. 7.5 - Prob. 40ECh. 7.5 - Ordering Forces Verify your answer to Exercise 40...Ch. 7.5 - Prob. 42ECh. 7.5 - Boyle's Law In Exercises 43 and 44, find the work...Ch. 7.5 - Prob. 44ECh. 7.5 - Prob. 45ECh. 7.5 - Prob. 46ECh. 7.5 - Prob. 47ECh. 7.5 - Prob. 48ECh. 7.5 - Prob. 49ECh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - Center of Mass of a Linear System In Exercises...Ch. 7.6 - Prob. 8ECh. 7.6 - Equilibrium of a Linear System In Exercises 9 and...Ch. 7.6 - Equilibrium of a Linear System In Exercises 9 and...Ch. 7.6 - Center of Mass of a Two-Dimensional System In...Ch. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Prob. 16ECh. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Prob. 18ECh. 7.6 - Prob. 19ECh. 7.6 - Prob. 20ECh. 7.6 - Prob. 21ECh. 7.6 - Prob. 22ECh. 7.6 - Prob. 23ECh. 7.6 - Prob. 24ECh. 7.6 - Center of Mass of a Planar Lamina In Exercises...Ch. 7.6 - Prob. 26ECh. 7.6 - Prob. 27ECh. 7.6 - Prob. 28ECh. 7.6 - Prob. 29ECh. 7.6 - Prob. 30ECh. 7.6 - Finding the Center of Mass In Exercises 31-34,...Ch. 7.6 - Finding the Center of Mass In Exercises 31-34,...Ch. 7.6 - Finding the Center of Mass In Exercises 31-34,...Ch. 7.6 - Finding the Center of Mass In Exercises 31-34,...Ch. 7.6 - Prob. 35ECh. 7.6 - Finding the Center of Mass Find the center of mass...Ch. 7.6 - Finding Volume by the Theorem of Pappus In...Ch. 7.6 - Prob. 38ECh. 7.6 - Finding Volume by the Theorem of Pappus In...Ch. 7.6 - Prob. 40ECh. 7.6 - Prob. 41ECh. 7.6 - Prob. 42ECh. 7.6 - Prob. 43ECh. 7.6 - Prob. 44ECh. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Prob. 48ECh. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Centroid of a Common Region In Exercises 45-50,...Ch. 7.6 - Prob. 51ECh. 7.6 - Prob. 52ECh. 7.6 - Modeling Data The manufacturer of glass for a...Ch. 7.6 - Prob. 54ECh. 7.6 - Prob. 55ECh. 7.6 - Second Theorem of Pappus In Exercises 55 and 56,...Ch. 7.6 - Prob. 57ECh. 7.6 - Prob. 58ECh. 7.6 - Prob. 59ECh. 7.7 - Prob. 1ECh. 7.7 - Prob. 2ECh. 7.7 - Prob. 3ECh. 7.7 - Prob. 4ECh. 7.7 - Prob. 5ECh. 7.7 - Prob. 6ECh. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - Prob. 9ECh. 7.7 - Prob. 10ECh. 7.7 - Fluid Force on a Tank Wall In Exercises 914, find...Ch. 7.7 - Fluid Force on a Tank Wall In Exercises 914, find...Ch. 7.7 - Fluid Force on a Tank Wall In Exercises 914, find...Ch. 7.7 - Fluid Force on a Tank Wall In Exercises 914, find...Ch. 7.7 - Prob. 15ECh. 7.7 - Fluid Force of Water In Exercises 15-18, find the...Ch. 7.7 - Fluid Force of Water In Exercises 1518, find the...Ch. 7.7 - Fluid Force of Water In Exercises 1518, find the...Ch. 7.7 - Prob. 19ECh. 7.7 - Force on a Concrete formIn Exercises 1922, the...Ch. 7.7 - Prob. 21ECh. 7.7 - Prob. 22ECh. 7.7 - Fluid Force of Gasoline A cylindrical gasoline...Ch. 7.7 - Prob. 24ECh. 7.7 - Prob. 25ECh. 7.7 - Prob. 26ECh. 7.7 - Prob. 27ECh. 7.7 - HOW DO YOU SEE IT? Two identical semicircular...Ch. 7.7 - Fluid Force on a Circular Plate A circular plate...Ch. 7.7 - Fluid Force on a Circular Plate Use the result of...Ch. 7.7 - Fluid Force on a Rectangular Plate A rectangular...Ch. 7.7 - Fluid Force on a Rectangular Plate Use the result...Ch. 7.7 - Submarine Porthole A square porthole on a vertical...Ch. 7.7 - Prob. 34ECh. 7.7 - Modeling Data The vertical stern of a boat...Ch. 7.7 - Prob. 36ECh. 7 - Finding the Area of a RegionIn Exercises 110,...Ch. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Finding the Area of a RegionIn Exercises 1-10,...Ch. 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 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Propulsion Neglecting air resistance and the...Ch. 7 - Pumping Water A water well has an 8-inch diameter...Ch. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Prob. 39RECh. 7 - Prob. 40RECh. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Center of Mass of a Planar Lamina In Exercises 43...Ch. 7 - Prob. 44RECh. 7 - Finding the Center of Mass Introduce an...Ch. 7 - Finding Volume Use the Theorem of Pappus to find...Ch. 7 - Prob. 47RECh. 7 - Prob. 48RECh. 7 - Prob. 49RECh. 7 - Prob. 50RECh. 7 - Submarine Porthole A circular porthole on a...Ch. 7 - Prob. 1PSCh. 7 - Center of Mass of a Lamina Let L be the lamina of...Ch. 7 - Dividing a Region Let R be the region bounded by...Ch. 7 - Surface Area Graph the curve 8y2=x2(1x2) Use a...Ch. 7 - Centroid A blade on an industrial fan has the...Ch. 7 - Prob. 6PSCh. 7 - Volume A rectangle R of length l and width w is...Ch. 7 - Prob. 8PSCh. 7 - Prob. 9PSCh. 7 - Using a Function Let f be rectifiable on the...Ch. 7 - Prob. 11PSCh. 7 - Prob. 12PSCh. 7 - Prob. 13PSCh. 7 - Prob. 14PSCh. 7 - Consumer and Producer Surplus In Exercises 15 and...Ch. 7 - Consumer and Producer Surplus In Exercises 15 and...Ch. 7 - Prob. 17PS
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