Calculus Volume 2
17th Edition
ISBN: 9781938168062
Author: Gilbert Strang, Edwin Jed Herman
Publisher: OpenStax
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Textbook Question
Chapter 2, Problem 452RE
For the following exercises, find the requested arc lengths.
452. The length of x for y = cosh(x) from x = 0 to x = 2.
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Question 3:
A sealed flask at room temperature contains a mixture of neon (Ne) and nitrogen (N2)
gases.
Ne has a mass of 3.25 g and exerts a pressure of 48.2 torr.
.
N2 contributes a pressure of 142 torr.
• What is the mass of the N2 in the flask?
• Atomic mass of Ne = 20.1797 g/mol
• Atomic mass of N = 14.0067 g/mol
Solution:
We will use the Ideal Gas Law to determine the number of moles of each gas and
calculate the mass of N2.
PV = nRT
where:
• P = total pressure
•
V volume of the flask (same for both gases)
n = number of moles of gas
•
R 0.0821 L atm/mol K
• T = Room temperature (assume 298 K)
Since both gases are in the same flask, their partial pressures correspond to their mole
fractions.
Step 1: Convert Pressures to Atmospheres
48.2
PNe
= 0.0634 atm
760
142
PN2
=
= 0.1868 atm
760
Step 2: Determine Moles of Ne
nNe =
mass
molar mass
3.25
nNe
20.1797
nne 0.1611 mol
Step 3: Use Partial Pressure Ratio to Find n
Suppose
a = p²¹...p
be the canonical factorization. Then the sum of all the factors of a, denoted by
σ(a) is given by
o(a) = II
+ k₂+1
P -1
Pi - 1
(you don't need to prove this).
(a) Let a = 2³ × 7². Find σ(a), which the sum of all the factors a.
Chapter 2 Solutions
Calculus Volume 2
Ch. 2.1 - For the following exercises, determine the area of...Ch. 2.1 - For the following exercises, determine the area of...Ch. 2.1 - For the following exercises, split the region...Ch. 2.1 - For the following exercises, split the region...Ch. 2.1 - For the following exercises, determine the area of...Ch. 2.1 - For the following exercises, determine the area of...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...
Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, graph the equations...Ch. 2.1 - For the following exercises, find the exact area...Ch. 2.1 - For the following exercises, find the exact area...Ch. 2.1 - For the following exercises, find the exact area...Ch. 2.1 - For the following exercises, find the exact area...Ch. 2.1 - For the following exercises, find the exact area...Ch. 2.1 - For the following exercises, find the exact area...Ch. 2.1 - For the following exercises, find the exact area...Ch. 2.1 - 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Explain when you would use the disk method versus...Ch. 2.2 - For the following exercises, draw a typical slice...Ch. 2.2 - For the following exercises, draw a typical slice...Ch. 2.2 - For the following exercises, draw a typical slice...Ch. 2.2 - For the following exercises, draw a typical slice...Ch. 2.2 - For the following exercises, draw a typical slice...Ch. 2.2 - For the following exercises, draw an outline of...Ch. 2.2 - For the following exercises, draw an outline of...Ch. 2.2 - For the following exercises, draw an outline of...Ch. 2.2 - For the following exercises, draw an outline of...Ch. 2.2 - For the following exercises, draw an outline of...Ch. 2.2 - For the following exercises, draw an outline of...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - 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For the following exercises, draw the region...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - For the following exercises, draw the region...Ch. 2.2 - Yogurt containers can be shaped like frustums....Ch. 2.2 - Rotate the ellipse (x2/a2)+(y2/b2)=1 around the...Ch. 2.2 - Rotate the ellipse (x2/a2)+(y2/b2)=1 around the...Ch. 2.2 - A better approximation of the volume of a football...Ch. 2.2 - What is the volume of the Bundt cake that comes...Ch. 2.2 - For the following exercises, find the volume of...Ch. 2.2 - For the following exercises, find the volume of...Ch. 2.2 - For the following exercises, find the volume of...Ch. 2.2 - For the following exercises, find the volume of...Ch. 2.2 - For the following exercises, find the volume of...Ch. 2.2 - For the following exercises, find the volume of...Ch. 2.3 - For the following exercise, find the volume...Ch. 2.3 - For the following exercise, find the volume...Ch. 2.3 - For the following exercise, find the volume...Ch. 2.3 - For the following exercise, find the volume...Ch. 2.3 - For the following exercise, find the volume...Ch. 2.3 - For the following exercise, find the volume...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, use shells to find...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - For the following exercises, find the volume...Ch. 2.3 - 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For the following exercises, find the Length of...Ch. 2.4 - Pick an arbitrary linear function x = g(y) over...Ch. 2.4 - Find the surface area of the volume generated when...Ch. 2.4 - Find the surface area of the volume generated when...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the Lengths of...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - For the following exercises, find the surface area...Ch. 2.4 - 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For the following exercises, find the work done....Ch. 2.5 - For the following exercises, find the work done....Ch. 2.5 - For the following exercises, find the work done....Ch. 2.5 - For the following exercises, find the work done....Ch. 2.5 - For the following exercises, find the work done....Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.5 - For the following exercises, find the mass of the...Ch. 2.6 - The Grand Canyon Skywalk opened to the public on...Ch. 2.6 - The Grand Canyon Skywalk opened to the public on...Ch. 2.6 - The Grand Canyon Skywalk opened to the public on...Ch. 2.6 - The Grand Canyon Skywalk opened to the public on...Ch. 2.6 - The Grand Canyon Skywalk opened to the public on...Ch. 2.6 - The Grand Canyon Skywalk opened to the public on...Ch. 2.6 - For the following exercises, calculate the center...Ch. 2.6 - For the following exercises, calculate the center...Ch. 2.6 - For the following exercises, calculate the center...Ch. 2.6 - For the following exercises, calculate the center...Ch. 2.6 - For the following exercises, calculate the center...Ch. 2.6 - For the following exercises, calculate the center...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, compute the center of...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use the theorem of...Ch. 2.6 - For the following exercises, use the theorem of...Ch. 2.6 - For the following exercises, use the theorem of...Ch. 2.6 - For the following exercises, use the theorem of...Ch. 2.6 - For the following exercises, use the theorem of...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - For the following exercises, use a calculator to...Ch. 2.6 - Find the generalized center of mass in the sliver...Ch. 2.6 - Find the generalized center of mass between y =...Ch. 2.6 - Find the generalized center of mass between y = b...Ch. 2.6 - Use the theorem of Pappus to find the volume of a...Ch. 2.6 - Find the center of mass (x,y) for a thin wire...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the indefinite...Ch. 2.7 - For the following exercises, find the indefinite...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the derivative...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - For the following exercises, find the definite or...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - Forthe following exercises, compute dy/dx by...Ch. 2.7 - For the following exercises, evaluate by any...Ch. 2.7 - For the following exercises, evaluate by any...Ch. 2.7 - For the following exercises, evaluate by any...Ch. 2.7 - For the following exercises, evaluate by any...Ch. 2.7 - For the following exercises, evaluate by any...Ch. 2.7 - For the following exercises, use the function ln...Ch. 2.7 - For the following exercises, use the function ln...Ch. 2.7 - For the following exercises, use the function ln...Ch. 2.7 - For the following exercises, use the function ln...Ch. 2.7 - For the following exercises, use the function ln...Ch. 2.7 - Find the area of the hyperbolic quarter-circle...Ch. 2.7 - If you are unable to find intersection points...Ch. 2.7 - If you are unable to find intersection points...Ch. 2.7 - For the following exercises, verify the...Ch. 2.7 - For the following exercises, verify the...Ch. 2.7 - For the following exercises, verify the...Ch. 2.7 - For the following exercises, verify the...Ch. 2.7 - For the following exercises, verify the...Ch. 2.8 - True or False? If true, prove it. If false, find...Ch. 2.8 - True or False? If true, prove it. If false, find...Ch. 2.8 - True or False? If true, prove it. If false, find...Ch. 2.8 - True or False? If true, prove it. If false, find...Ch. 2.8 - For the following exercises, use y=y0ekt . 352.If...Ch. 2.8 - For the following exercises, use y=y0ekt . 353.If...Ch. 2.8 - For the following exercises, use y=y0ekt . 354.How...Ch. 2.8 - For the following exercises, use y=y0ekt . 355. If...Ch. 2.8 - For the following exercises, use y=y0ekt . 356....Ch. 2.8 - For the following exercises, use y=y0ekt . 357.The...Ch. 2.8 - For the following exercises, use y=y0ekt ....Ch. 2.8 - For the following exercises, use y=y0ekt . 359....Ch. 2.8 - For the following exercises, use y=y0ekt . 360.If...Ch. 2.8 - For the following exercises, use y=y0ekt . 361.If...Ch. 2.8 - For the following exercises, use y=y0ekt . 362. If...Ch. 2.8 - For the following exercises, use y=y0ekt ....Ch. 2.8 - For the following exercises, use y=y0ekt . 364.If...Ch. 2.8 - For the following exercises, use y=y0ekt . 365.You...Ch. 2.8 - For the following exercises, use y=y0ekt . 366.You...Ch. 2.8 - For the following exercises, use y=y0ekt . 367.You...Ch. 2.8 - For the following exercises, use y=y0ekt . 368....Ch. 2.8 - For the following exercises, use y=y0ekt . 369....Ch. 2.8 - For the next set of exercises, use the following...Ch. 2.8 - For the next set of exercises, use the following...Ch. 2.8 - For the next set of exercises, use the following...Ch. 2.8 - For the next set of exercises, use the following...Ch. 2.8 - For the next set of exercises, use the following...Ch. 2.8 - For the next set of exercises, use the following...Ch. 2.8 - For the next set of exercises, use the following...Ch. 2.9 - [T] Find expressions for cosh x + sinh x and cosh...Ch. 2.9 - From the definitions of cosh(x) and sinh(x), find...Ch. 2.9 - Show that cosh(x) and sinh(x) satisfy y" = y.Ch. 2.9 - Use the quotient rule to verify that tanh(x)' =...Ch. 2.9 - Derive cosh2(x) + sinh2(x) = cosh(2x) from the...Ch. 2.9 - Take the derivative of the previous expression to...Ch. 2.9 - Prove sinh(x + y) = sinh(x)cosh(y) +...Ch. 2.9 - Take the derivative of the previous expression to...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the derivatives...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, find the...Ch. 2.9 - For the following exercises, use the fact that a...Ch. 2.9 - For the following exercises, use the fact that a...Ch. 2.9 - For the following exercises, use the fact that a...Ch. 2.9 - For the following exercises, use this scenario: A...Ch. 2.9 - For the following exercises, use this scenario: A...Ch. 2.9 - For the following exercises, use this scenario: A...Ch. 2.9 - For the following exercises, solve each problem....Ch. 2.9 - For the following exercises, solve each problem....Ch. 2.9 - For the following exercises, solve each problem....Ch. 2.9 - For the following exercises, solve each problem....Ch. 2.9 - For the following exercises, solve each problem....Ch. 2.9 - For the following exercises, solve each problem....Ch. 2.9 - For the following exercises, solve each problem....Ch. 2.9 - For the following exercises, solve each problem....Ch. 2.9 - For the following exercises, solve each problem....Ch. 2.9 - For the following exercises, solve each problem....Ch. 2 - True or False? 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