
University Calculus: Early Transcendentals (3rd Edition)
3rd Edition
ISBN: 9780321999580
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Chapter 15.1, Problem 10E
To determine
Evaluate the integral
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Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
Chapter 15 Solutions
University Calculus: Early Transcendentals (3rd Edition)
Ch. 15.1 - Match the vector equations in Exercises 1–8 with...Ch. 15.1 - Match the vector equations in Exercises 1–8 with...Ch. 15.1 - Match the vector equations in Exercises 1–8 with...Ch. 15.1 - Match the vector equations in Exercises 1–8 with...Ch. 15.1 - Match the vector equations in Exercises 1–8 with...Ch. 15.1 - Match the vector equations in Exercises 1–8 with...Ch. 15.1 - Match the vector equations in Exercises 1–8 with...Ch. 15.1 - Prob. 8ECh. 15.1 - Evaluate ∫C (x + y) ds, where C is the...Ch. 15.1 - Evaluate ∫C (x − y + z − 2) ds, where C is the...
Ch. 15.1 - Evaluate ∫C (xy + y + z) ds along the curve r(t) =...Ch. 15.1 - Evaluate Cx2+y2ds along the curve r(t) = (4 cos...Ch. 15.1 - Find the line integral of f(x, y, z) = x + y + z...Ch. 15.1 - Find the line integral of over the curve r(t) =...Ch. 15.1 - Integrate over the path C1 followed by C2 from...Ch. 15.1 - Prob. 16ECh. 15.1 - Integrate f(x, y, z) = (x + y + z)/(x2+ y2+ z2)...Ch. 15.1 - Integrate over the circle r(t) = (a cos t)j + (a...Ch. 15.1 - Evaluate ∫C x ds, where C is
the straight-line...Ch. 15.1 - Evaluate , where C is
the straight-line segment x...Ch. 15.1 - Find the line integral of along the curve r(t) =...Ch. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Find the line integral of along the curve , 1/2 ≤...Ch. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - Prob. 28ECh. 15.1 - In Exercises 27–30, integrate f over the given...Ch. 15.1 - In Exercises 27–30, integrate f over the given...Ch. 15.1 - Prob. 31ECh. 15.1 - Prob. 32ECh. 15.1 - Mass of a wire Find the mass of a wire that lies...Ch. 15.1 - Center of mass of a curved wire A wire of density ...Ch. 15.1 - Mass of wire with variable density Find the mass...Ch. 15.1 - Center of mass of wire with variable density Find...Ch. 15.1 - Prob. 37ECh. 15.1 - Prob. 38ECh. 15.1 - Prob. 39ECh. 15.1 - Wire of constant density A wire of constant...Ch. 15.1 - Prob. 41ECh. 15.1 - Prob. 42ECh. 15.2 - Find the gradient fields of the functions in...Ch. 15.2 - Find the gradient fields of the functions in...Ch. 15.2 - Find the gradient fields of the functions in...Ch. 15.2 - Find the gradient fields of the functions in...Ch. 15.2 - Give a formula F = M(x, y)i + N(x, y)j for the...Ch. 15.2 - Give a formula F = M(x, y)i + N(x, y)j for the...Ch. 15.2 - In Exercises 7−12, find the line integrals of F...Ch. 15.2 - In Exercises 7−12, find the line integrals of F...Ch. 15.2 - In Exercises 7−12, find the line integrals of F...Ch. 15.2 - In Exercises 7−12, find the line integrals of F...Ch. 15.2 - Line Integrals of Vector Fields
In Exercises 7−12,...Ch. 15.2 - Line Integrals of Vector Fields
In Exercises 7−12,...Ch. 15.2 - In Exercises 1316, find the line integrals along...Ch. 15.2 - In Exercises 13–16, find the line integrals along...Ch. 15.2 - In Exercises 13–16, find the line integrals along...Ch. 15.2 - In Exercises 13–16, find the line integrals along...Ch. 15.2 - Along the curve , , evaluate each of the following...Ch. 15.2 - Along the curve , , evaluate each of the following...Ch. 15.2 - In Exercises 19–22, find the work done by F over...Ch. 15.2 - In Exercises 19–22, find the work done by F over...Ch. 15.2 - In Exercises 19–22, find the work done by F over...Ch. 15.2 - In Exercises 19–22, find the work done by F over...Ch. 15.2 - Evaluate along the curve from (–1, 1) to (2,...Ch. 15.2 - Evaluate counterclockwise around the triangle...Ch. 15.2 - Evaluate CFTds for the vector field F=x2iyj along...Ch. 15.2 - Evaluate for the vector field counterclockwise...Ch. 15.2 - Work Find the work done by the force F = xyi + (y...Ch. 15.2 - Work Find the work done by the gradient of f(x, y)...Ch. 15.2 - Circulation and flux Find the circulation and flux...Ch. 15.2 - Flux across a circle Find the flux of the...Ch. 15.2 - In Exercises 31–34, find the circulation and flux...Ch. 15.2 - In Exercises 31–34, find the circulation and flux...Ch. 15.2 - In Exercises 31–34, find the circulation and flux...Ch. 15.2 - In Exercises 31–34, find the circulation and flux...Ch. 15.2 - Flow integrals Find the flow of the velocity field...Ch. 15.2 - Flux across a triangle Find the flux of the field...Ch. 15.2 - Find the flow of the velocity field F = y2i + 2xyj...Ch. 15.2 - Find the circulation of the field F = yi + (x +...Ch. 15.2 - Spin field Draw the spin field
(see Figure 15.13)...Ch. 15.2 - Prob. 40ECh. 15.2 - Prob. 41ECh. 15.2 - Prob. 42ECh. 15.2 - Prob. 43ECh. 15.2 - Prob. 44ECh. 15.2 - Prob. 45ECh. 15.2 - Prob. 46ECh. 15.2 - Prob. 47ECh. 15.2 - Prob. 48ECh. 15.2 - Prob. 49ECh. 15.2 - Prob. 50ECh. 15.2 - Prob. 51ECh. 15.2 - Prob. 52ECh. 15.2 - Flow along a curve The field F = xyi + yj − yzk is...Ch. 15.2 - Prob. 54ECh. 15.3 - Which fields in Exercises 1–6 are conservative,...Ch. 15.3 - Which fields in Exercises 1–6 are conservative,...Ch. 15.3 - Which fields in Exercises 1–6 are conservative,...Ch. 15.3 - Which fields in Exercises 1–6 are conservative,...Ch. 15.3 - Which fields in Exercises 1−6 are conservative,...Ch. 15.3 - Which fields in Exercises 1−6 are conservative,...Ch. 15.3 - Finding Potential Functions In Exercises 712, find...Ch. 15.3 -
In Exercises 7–12, find a potential function f...Ch. 15.3 - In Exercises 7–12, find a potential function f for...Ch. 15.3 - In Exercises 7–12, find a potential function f for...Ch. 15.3 - In Exercises 7–12, find a potential function f for...Ch. 15.3 - In Exercises 7–12, find a potential function f for...Ch. 15.3 - In Exercises 13–17, show that the differential...Ch. 15.3 - In Exercises 13–17, show that the differential...Ch. 15.3 - In Exercises 13–17, show that the differential...Ch. 15.3 - In Exercises 13–17, show that the differential...Ch. 15.3 - In Exercises 13–17, show that the differential...Ch. 15.3 - Although they are not defined on all of space R3,...Ch. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - Prob. 21ECh. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.3 - Prob. 25ECh. 15.3 - Prob. 26ECh. 15.3 - In Exercises 27 and 28, find a potential function...Ch. 15.3 - In Exercises 27 and 28, find a potential function...Ch. 15.3 - Work along different paths Find the work done by F...Ch. 15.3 - Work along different paths Find the work done by F...Ch. 15.3 - Evaluating a work integral two ways Let F =...Ch. 15.3 - Prob. 32ECh. 15.3 - Exact differential form How are the constants a,...Ch. 15.3 - Prob. 34ECh. 15.3 - Prob. 35ECh. 15.3 - Prob. 36ECh. 15.3 - Prob. 37ECh. 15.3 - Prob. 38ECh. 15.4 - In Exercises 710, verify the conclusion of Green’s...Ch. 15.4 - In Exercises 7–10, verify the conclusion of...Ch. 15.4 - In Exercises 7–10, verify the conclusion of...Ch. 15.4 - In Exercises 7–10, verify the conclusion of...Ch. 15.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 15.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 15.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 15.4 - Prob. 8ECh. 15.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 15.4 - Prob. 10ECh. 15.4 - Prob. 11ECh. 15.4 - Prob. 12ECh. 15.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 15.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 15.4 - Find the counterclockwise circulation and outward...Ch. 15.4 - Prob. 16ECh. 15.4 - Prob. 17ECh. 15.4 - Prob. 18ECh. 15.4 - Prob. 19ECh. 15.4 - Prob. 20ECh. 15.4 - Apply Green’s Theorem to evaluate the integrals in...Ch. 15.4 - Prob. 22ECh. 15.4 - Apply Green’s Theorem to evaluate the integrals in...Ch. 15.4 - Apply Green’s Theorem to evaluate the integrals in...Ch. 15.4 - Prob. 25ECh. 15.4 - Prob. 26ECh. 15.4 - Prob. 27ECh. 15.4 - Prob. 28ECh. 15.4 - Prob. 29ECh. 15.4 - Prob. 30ECh. 15.4 - Prob. 31ECh. 15.4 - Prob. 32ECh. 15.4 - Prob. 33ECh. 15.4 - Prob. 34ECh. 15.4 - Prob. 35ECh. 15.4 - Prob. 36ECh. 15.4 - Prob. 37ECh. 15.4 - Prob. 38ECh. 15.4 - Regions with many holes Green’s Theorem holds for...Ch. 15.4 - Prob. 40ECh. 15.4 - Prob. 41ECh. 15.4 - Prob. 42ECh. 15.5 - In Exercises 1–16, find a parametrization of the...Ch. 15.5 - Prob. 2ECh. 15.5 - Prob. 3ECh. 15.5 - Prob. 4ECh. 15.5 - In Exercises 1–16, find a parametrization of the...Ch. 15.5 - Prob. 6ECh. 15.5 - In Exercises 1–16, find a parametrization of the...Ch. 15.5 - Prob. 8ECh. 15.5 - Prob. 9ECh. 15.5 - Prob. 10ECh. 15.5 - In Exercises 1–16, find a parametrization of the...Ch. 15.5 - Prob. 12ECh. 15.5 - In Exercises 1–16, find a parametrization of the...Ch. 15.5 - Prob. 14ECh. 15.5 - Prob. 15ECh. 15.5 - Prob. 16ECh. 15.5 - In Exercises 17–26, use a parametrization to...Ch. 15.5 - Prob. 18ECh. 15.5 - Prob. 19ECh. 15.5 - Prob. 20ECh. 15.5 - Prob. 21ECh. 15.5 - In Exercises 17–26, use a parametrization to...Ch. 15.5 - Prob. 23ECh. 15.5 - In Exercises 17–26, use a parametrization to...Ch. 15.5 - Prob. 25ECh. 15.5 - In Exercises 17–26, use a parametrization to...Ch. 15.5 - Prob. 27ECh. 15.5 - Prob. 28ECh. 15.5 - Prob. 29ECh. 15.5 - Prob. 30ECh. 15.5 - Prob. 31ECh. 15.5 - Prob. 32ECh. 15.5 - Parametrization of an ellipsoid The...Ch. 15.5 - Prob. 34ECh. 15.5 - Prob. 35ECh. 15.5 - Prob. 36ECh. 15.5 - Prob. 37ECh. 15.5 - Prob. 38ECh. 15.5 - Prob. 39ECh. 15.5 - Prob. 40ECh. 15.5 - Prob. 41ECh. 15.5 - Prob. 42ECh. 15.5 - Prob. 43ECh. 15.5 - Find the area of the upper portion of the cylinder...Ch. 15.5 - Prob. 45ECh. 15.5 - Prob. 46ECh. 15.5 - Prob. 47ECh. 15.5 - Prob. 48ECh. 15.5 - Prob. 49ECh. 15.5 - Prob. 50ECh. 15.5 - Prob. 51ECh. 15.5 - Prob. 52ECh. 15.5 - Prob. 53ECh. 15.5 - Prob. 54ECh. 15.5 - Prob. 55ECh. 15.5 - Prob. 56ECh. 15.6 - In Exercises 1–8, integrate the given function...Ch. 15.6 - In Exercises 18, integrate the given function over...Ch. 15.6 - In Exercises 1–8, integrate the given function...Ch. 15.6 - In Exercises 1–8, integrate the given function...Ch. 15.6 - Prob. 5ECh. 15.6 - Prob. 6ECh. 15.6 - Prob. 7ECh. 15.6 - Prob. 8ECh. 15.6 - Prob. 9ECh. 15.6 - Prob. 10ECh. 15.6 - Prob. 11ECh. 15.6 - Prob. 12ECh. 15.6 - Prob. 13ECh. 15.6 - Prob. 14ECh. 15.6 - Integrate G(x, y, z) = z − x over the portion of...Ch. 15.6 - Prob. 16ECh. 15.6 - Prob. 17ECh. 15.6 - Prob. 18ECh. 15.6 - In Exercises 19–28, use a parametrization to find...Ch. 15.6 - Prob. 20ECh. 15.6 - Prob. 21ECh. 15.6 - Prob. 22ECh. 15.6 - Prob. 23ECh. 15.6 - Prob. 24ECh. 15.6 - Prob. 25ECh. 15.6 - Prob. 26ECh. 15.6 - In Exercises 19–28, use a parametrization to find...Ch. 15.6 - Prob. 28ECh. 15.6 - Prob. 29ECh. 15.6 - Prob. 30ECh. 15.6 - Prob. 31ECh. 15.6 - Prob. 32ECh. 15.6 - Prob. 33ECh. 15.6 - Prob. 34ECh. 15.6 - Prob. 35ECh. 15.6 - Prob. 36ECh. 15.6 - Find the flux of the field through the surface...Ch. 15.6 - Prob. 38ECh. 15.6 - Prob. 39ECh. 15.6 - Prob. 40ECh. 15.6 - Prob. 41ECh. 15.6 - Prob. 42ECh. 15.6 - Prob. 43ECh. 15.6 - Prob. 44ECh. 15.6 - Prob. 45ECh. 15.6 - Prob. 46ECh. 15.7 - In Exercises 7–12, use the surface integral in...Ch. 15.7 - Prob. 2ECh. 15.7 - Prob. 3ECh. 15.7 - Prob. 4ECh. 15.7 - Prob. 5ECh. 15.7 - Prob. 6ECh. 15.7 - Prob. 7ECh. 15.7 - Prob. 8ECh. 15.7 - Prob. 9ECh. 15.7 - Prob. 10ECh. 15.7 - Prob. 11ECh. 15.7 - Prob. 12ECh. 15.7 - In Exercises 19–24, use the surface integral in...Ch. 15.7 - Prob. 14ECh. 15.7 - In Exercises 19–24, use the surface integral in...Ch. 15.7 - Prob. 16ECh. 15.7 - Prob. 17ECh. 15.7 - Prob. 18ECh. 15.7 - Prob. 19ECh. 15.7 - Verify Stokes’ Theorem for the vector field F =...Ch. 15.7 - Zero circulation Use Equation (8) and Stokes’...Ch. 15.7 - Prob. 22ECh. 15.7 - Prob. 23ECh. 15.7 - Prob. 24ECh. 15.7 - Prob. 25ECh. 15.7 - Does Stokes’ Theorem say anything special about...Ch. 15.7 - Let R be a region in the xy-plane that is bounded...Ch. 15.7 - Zero curl, yet the field is not conservative Show...Ch. 15.8 - Prob. 1ECh. 15.8 - Prob. 2ECh. 15.8 - Prob. 3ECh. 15.8 - Prob. 4ECh. 15.8 - Prob. 5ECh. 15.8 - In Exercises 920, use the Divergence Theorem to...Ch. 15.8 - Prob. 7ECh. 15.8 - Prob. 8ECh. 15.8 - Prob. 9ECh. 15.8 - Prob. 10ECh. 15.8 - Prob. 11ECh. 15.8 - Prob. 12ECh. 15.8 - Prob. 13ECh. 15.8 - Prob. 14ECh. 15.8 - Prob. 15ECh. 15.8 - Prob. 16ECh. 15.8 - Prob. 17ECh. 15.8 - Prob. 18ECh. 15.8 - Prob. 19ECh. 15.8 - Prob. 20ECh. 15.8 - Prob. 21ECh. 15.8 - Prob. 22ECh. 15.8 - Prob. 23ECh. 15.8 - Compute the net outward flux of the vector field F...Ch. 15.8 - Prob. 25ECh. 15.8 - Prob. 26ECh. 15.8 - Prob. 27ECh. 15.8 - Prob. 28ECh. 15.8 - Prob. 29ECh. 15.8 - Prob. 30ECh. 15 - Prob. 1GYRCh. 15 - Prob. 2GYRCh. 15 - Prob. 3GYRCh. 15 - Prob. 4GYRCh. 15 - Prob. 5GYRCh. 15 - Prob. 6GYRCh. 15 - What is special about path independent fields?
Ch. 15 - Prob. 8GYRCh. 15 - Prob. 9GYRCh. 15 - Prob. 10GYRCh. 15 - Prob. 11GYRCh. 15 - Prob. 12GYRCh. 15 - What is an oriented surface? What is the surface...Ch. 15 - Prob. 14GYRCh. 15 - Prob. 15GYRCh. 15 - Prob. 16GYRCh. 15 - Prob. 17GYRCh. 15 - Prob. 18GYRCh. 15 - Prob. 1PECh. 15 - The accompanying figure shows three polygonal...Ch. 15 - Prob. 3PECh. 15 - Prob. 4PECh. 15 - Prob. 5PECh. 15 - Prob. 6PECh. 15 - Prob. 7PECh. 15 - Prob. 8PECh. 15 - Prob. 9PECh. 15 - Prob. 10PECh. 15 - Prob. 11PECh. 15 - Prob. 12PECh. 15 - Prob. 13PECh. 15 - Prob. 14PECh. 15 - Prob. 15PECh. 15 - Prob. 16PECh. 15 - Prob. 17PECh. 15 - Prob. 18PECh. 15 - Prob. 19PECh. 15 - Prob. 20PECh. 15 - Prob. 21PECh. 15 - Prob. 22PECh. 15 - Prob. 23PECh. 15 - Prob. 24PECh. 15 - Prob. 25PECh. 15 - Prob. 26PECh. 15 - Prob. 27PECh. 15 - Prob. 28PECh. 15 - Prob. 29PECh. 15 - Prob. 30PECh. 15 - Prob. 31PECh. 15 - Prob. 32PECh. 15 - Prob. 33PECh. 15 - Prob. 34PECh. 15 - Prob. 35PECh. 15 - Prob. 36PECh. 15 - Prob. 37PECh. 15 - Prob. 38PECh. 15 - Prob. 39PECh. 15 - Prob. 40PECh. 15 - Prob. 41PECh. 15 - Prob. 42PECh. 15 - Prob. 43PECh. 15 - Prob. 44PECh. 15 - Prob. 45PECh. 15 - Prob. 46PECh. 15 - Prob. 47PECh. 15 - Moment of inertia of a cube Find the moment of...Ch. 15 - Prob. 49PECh. 15 - Prob. 50PECh. 15 - Prob. 51PECh. 15 - Prob. 52PECh. 15 - Prob. 53PECh. 15 - In Exercises 53–56, find the outward flux of F...Ch. 15 - Prob. 55PECh. 15 - In Exercises 53–56, find the outward flux of F...Ch. 15 - Hemisphere, cylinder, and plane Let S be the...Ch. 15 - Prob. 58PECh. 15 - Prob. 59PECh. 15 - Prob. 60PECh. 15 - Prob. 1AAECh. 15 - Use the Green’s Theorem area formula in Exercises...Ch. 15 - Prob. 3AAECh. 15 - Use the Green’s Theorem area formula in Exercises...Ch. 15 - Prob. 5AAECh. 15 - Prob. 6AAECh. 15 - Prob. 7AAECh. 15 - Find the mass of a helicoids
r(r, ) = (r cos )i +...Ch. 15 - Prob. 9AAECh. 15 - Prob. 10AAECh. 15 - Prob. 11AAECh. 15 - Prob. 12AAECh. 15 - Prob. 13AAECh. 15 - Prob. 14AAECh. 15 - Prob. 15AAECh. 15 - Prob. 16AAECh. 15 - Prob. 17AAECh. 15 - Prob. 18AAE
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