EP THOMAS'CALCULUS,EARLY TRANS.-MYLAB
14th Edition
ISBN: 9780135961308
Author: Hass
Publisher: PEARSON CO
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Chapter 16.4, Problem 5E
To determine
Find the k-component of
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The spread of an infectious disease is often modeled using the following autonomous differential equation:
dI
-
- BI(N − I) − MI,
dt
where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of
transmission, and μ is the rate at which people recover from infection.
Close
a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria.
b) (5 points) For the equilbria in part a), determine whether each is stable or unstable.
c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the
dt
function by hand.) Identify the equilibria as stable or unstable in the graph.
d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.
Find the indefinite integral.
Check
Answer:
7x
4 + 1x
dx
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Chapter 16 Solutions
EP THOMAS'CALCULUS,EARLY TRANS.-MYLAB
Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Prob. 5ECh. 16.1 - Prob. 6ECh. 16.1 - Prob. 7ECh. 16.1 - Prob. 8ECh. 16.1 - Evaluate ∫C (x + y) ds, where C is the...Ch. 16.1 - Prob. 10E
Ch. 16.1 - Evaluate ∫C (xy + y + z) ds along the curve r(t) =...Ch. 16.1 - Evaluate along the curve r(t) = (4 cos t)i + (4...Ch. 16.1 - Find the line integral of f(x, y, z) = x + y + z...Ch. 16.1 - Prob. 14ECh. 16.1 - Prob. 15ECh. 16.1 - Integrate over the path C1 followed by C2...Ch. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Evaluate ∫C x ds, where C is
the straight-line...Ch. 16.1 - Evaluate , where C is
the straight-line segment x...Ch. 16.1 - Prob. 21ECh. 16.1 - Find the line integral of f(x, y) = x − y + 3...Ch. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Evaluate , where C is given in the accompanying...Ch. 16.1 - Prob. 27ECh. 16.1 - Prob. 28ECh. 16.1 - Prob. 29ECh. 16.1 - Prob. 30ECh. 16.1 - Find the area of one side of the “winding wall”...Ch. 16.1 - Prob. 32ECh. 16.1 - Prob. 33ECh. 16.1 - Center of mass of a curved wire A wire of density ...Ch. 16.1 - Prob. 35ECh. 16.1 - Prob. 36ECh. 16.1 - Prob. 37ECh. 16.1 - Prob. 38ECh. 16.1 - Prob. 39ECh. 16.1 - Prob. 40ECh. 16.1 - Prob. 41ECh. 16.1 - Prob. 42ECh. 16.2 - Find the gradient fields of the functions in...Ch. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - In Exercises 7−12, find the line integrals of F...Ch. 16.2 - Prob. 8ECh. 16.2 - Prob. 9ECh. 16.2 - Prob. 10ECh. 16.2 - Line Integrals of Vector Fields
In Exercises 7−12,...Ch. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - In Exercises 13–16, find the line integrals along...Ch. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.2 - In Exercises 19–22, find the work done by F over...Ch. 16.2 - Prob. 20ECh. 16.2 - Prob. 21ECh. 16.2 - Prob. 22ECh. 16.2 - Prob. 23ECh. 16.2 - Prob. 24ECh. 16.2 - Prob. 25ECh. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Prob. 29ECh. 16.2 - Prob. 30ECh. 16.2 - Prob. 31ECh. 16.2 - Prob. 32ECh. 16.2 - In Exercises 31–34, find the circulation and flux...Ch. 16.2 - Prob. 34ECh. 16.2 - Prob. 35ECh. 16.2 - Prob. 36ECh. 16.2 - Prob. 37ECh. 16.2 - Prob. 38ECh. 16.2 - Prob. 39ECh. 16.2 - Find the circulation of the field F = yi + (x +...Ch. 16.2 - Prob. 41ECh. 16.2 - Prob. 42ECh. 16.2 - Prob. 43ECh. 16.2 - Prob. 44ECh. 16.2 - Prob. 45ECh. 16.2 - Prob. 46ECh. 16.2 - Prob. 47ECh. 16.2 - Prob. 48ECh. 16.2 - A field of tangent vectors
Find a field G = P(x,...Ch. 16.2 - Prob. 50ECh. 16.2 - Prob. 51ECh. 16.2 - Prob. 52ECh. 16.2 - Prob. 53ECh. 16.2 - Work done by a radial force with constant...Ch. 16.2 - Prob. 55ECh. 16.2 - Prob. 56ECh. 16.2 - Prob. 57ECh. 16.2 - Prob. 58ECh. 16.2 - Circulation Find the circulation of F = 2xi + 2zj...Ch. 16.2 - Prob. 60ECh. 16.2 - Prob. 61ECh. 16.2 - Prob. 62ECh. 16.3 - Which fields in Exercises 1–6 are conservative,...Ch. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Finding Potential Functions
In Exercises 7–12,...Ch. 16.3 -
In Exercises 7–12, find a potential function f...Ch. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - Prob. 10ECh. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - Prob. 12ECh. 16.3 - Prob. 13ECh. 16.3 - Prob. 14ECh. 16.3 - Prob. 15ECh. 16.3 - Prob. 16ECh. 16.3 - Prob. 17ECh. 16.3 - Prob. 18ECh. 16.3 - Prob. 19ECh. 16.3 - Prob. 20ECh. 16.3 - Prob. 21ECh. 16.3 - Prob. 22ECh. 16.3 - Prob. 23ECh. 16.3 - Prob. 24ECh. 16.3 - Prob. 25ECh. 16.3 - Prob. 26ECh. 16.3 - Prob. 27ECh. 16.3 - Prob. 28ECh. 16.3 - Work along different paths Find the work done by F...Ch. 16.3 - Prob. 30ECh. 16.3 - Prob. 31ECh. 16.3 - Integral along different paths Evaluate the line...Ch. 16.3 - Prob. 33ECh. 16.3 - Prob. 34ECh. 16.3 - Prob. 35ECh. 16.3 - Prob. 36ECh. 16.3 - Prob. 37ECh. 16.3 - Gravitational field
Find a potential function for...Ch. 16.4 - In Exercises 1–6, find the k-component of curl(F)...Ch. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.4 - Prob. 7ECh. 16.4 - In Exercises 7–10, verify the conclusion of...Ch. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - Prob. 15ECh. 16.4 - Prob. 16ECh. 16.4 - Prob. 17ECh. 16.4 - Prob. 18ECh. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.4 - Prob. 21ECh. 16.4 - Prob. 22ECh. 16.4 - Prob. 23ECh. 16.4 - Prob. 24ECh. 16.4 - Prob. 25ECh. 16.4 - Prob. 26ECh. 16.4 - Prob. 27ECh. 16.4 - Prob. 28ECh. 16.4 - Prob. 29ECh. 16.4 - Prob. 30ECh. 16.4 - Prob. 31ECh. 16.4 - Use the Green’s Theorem area formula given above...Ch. 16.4 - Use the Green’s Theorem area formula given above...Ch. 16.4 - Use the Green’s Theorem area formula given above...Ch. 16.4 - Prob. 35ECh. 16.4 - Prob. 36ECh. 16.4 - Prob. 37ECh. 16.4 - Prob. 38ECh. 16.4 - Prob. 39ECh. 16.4 - Prob. 40ECh. 16.4 - Prob. 41ECh. 16.4 - Prob. 42ECh. 16.4 - Prob. 43ECh. 16.4 - Prob. 44ECh. 16.4 - Prob. 45ECh. 16.4 - Prob. 46ECh. 16.4 - Prob. 47ECh. 16.4 - Prob. 48ECh. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - Prob. 2ECh. 16.5 - Prob. 3ECh. 16.5 - Prob. 4ECh. 16.5 - Prob. 5ECh. 16.5 - Prob. 6ECh. 16.5 - Prob. 7ECh. 16.5 - Prob. 8ECh. 16.5 - Prob. 9ECh. 16.5 - Prob. 10ECh. 16.5 - Prob. 11ECh. 16.5 - Prob. 12ECh. 16.5 - Prob. 13ECh. 16.5 - Prob. 14ECh. 16.5 - Prob. 15ECh. 16.5 - Prob. 16ECh. 16.5 - Prob. 17ECh. 16.5 - Prob. 18ECh. 16.5 - Prob. 19ECh. 16.5 - Prob. 20ECh. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - Prob. 23ECh. 16.5 - Prob. 24ECh. 16.5 - Prob. 25ECh. 16.5 - Prob. 26ECh. 16.5 - Prob. 27ECh. 16.5 - Prob. 28ECh. 16.5 - Prob. 29ECh. 16.5 - Prob. 30ECh. 16.5 - Prob. 31ECh. 16.5 - Prob. 32ECh. 16.5 - Prob. 33ECh. 16.5 - Prob. 34ECh. 16.5 - Prob. 35ECh. 16.5 - Prob. 36ECh. 16.5 - Prob. 37ECh. 16.5 - Prob. 38ECh. 16.5 - Prob. 39ECh. 16.5 - Prob. 40ECh. 16.5 - Prob. 41ECh. 16.5 - Find the area of the cap cut from the sphere x2 +...Ch. 16.5 - Prob. 43ECh. 16.5 - Prob. 44ECh. 16.5 - Prob. 45ECh. 16.5 - Prob. 46ECh. 16.5 - Prob. 47ECh. 16.5 - Prob. 48ECh. 16.5 - Prob. 49ECh. 16.5 - Prob. 50ECh. 16.5 - Prob. 51ECh. 16.5 - Find the area of the surfaces in Exercises...Ch. 16.5 - Prob. 53ECh. 16.5 - Prob. 54ECh. 16.5 - Prob. 55ECh. 16.5 - Prob. 56ECh. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - Prob. 5ECh. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - Prob. 7ECh. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - Prob. 9ECh. 16.6 - Prob. 10ECh. 16.6 - Prob. 11ECh. 16.6 - Prob. 12ECh. 16.6 - Prob. 13ECh. 16.6 - Prob. 14ECh. 16.6 - Prob. 15ECh. 16.6 - Integrate G(x, y, z) = x over the surface given by...Ch. 16.6 - Prob. 17ECh. 16.6 - Integrate G(x, y, z) = x – y – z over the portion...Ch. 16.6 - Prob. 19ECh. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - Prob. 21ECh. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - Prob. 25ECh. 16.6 - Prob. 26ECh. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - Prob. 28ECh. 16.6 - Prob. 29ECh. 16.6 - Prob. 30ECh. 16.6 - Prob. 31ECh. 16.6 - Prob. 32ECh. 16.6 - Prob. 33ECh. 16.6 - Prob. 34ECh. 16.6 - Prob. 35ECh. 16.6 - Prob. 36ECh. 16.6 - Prob. 37ECh. 16.6 - Prob. 38ECh. 16.6 - Prob. 39ECh. 16.6 - Prob. 40ECh. 16.6 - Prob. 41ECh. 16.6 - Prob. 42ECh. 16.6 - Prob. 43ECh. 16.6 - Prob. 44ECh. 16.6 - Prob. 45ECh. 16.6 - Prob. 46ECh. 16.6 - Prob. 47ECh. 16.6 - Prob. 48ECh. 16.6 - Prob. 49ECh. 16.6 - Prob. 50ECh. 16.7 - Prob. 1ECh. 16.7 - Prob. 2ECh. 16.7 - Prob. 3ECh. 16.7 - Prob. 4ECh. 16.7 - Prob. 5ECh. 16.7 - Prob. 6ECh. 16.7 - Prob. 7ECh. 16.7 - Prob. 8ECh. 16.7 - Prob. 9ECh. 16.7 - In Exercises 7–12, use the surface integral in...Ch. 16.7 - Prob. 11ECh. 16.7 - Prob. 12ECh. 16.7 - Prob. 13ECh. 16.7 - Prob. 14ECh. 16.7 - Prob. 15ECh. 16.7 - Evaluate
where S is the hemisphere x2 + y2 + z2 =...Ch. 16.7 - Prob. 17ECh. 16.7 - Prob. 18ECh. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - Prob. 20ECh. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - Prob. 22ECh. 16.7 - Prob. 23ECh. 16.7 - Prob. 24ECh. 16.7 - Prob. 25ECh. 16.7 - Verify Stokes’ Theorem for the vector field F =...Ch. 16.7 - Prob. 27ECh. 16.7 - Prob. 28ECh. 16.7 - Prob. 29ECh. 16.7 - Prob. 30ECh. 16.7 - Prob. 31ECh. 16.7 - Does Stokes’ Theorem say anything special about...Ch. 16.7 - Prob. 33ECh. 16.7 - Prob. 34ECh. 16.8 - In Exercises 1–8, find the divergence of the...Ch. 16.8 - Prob. 2ECh. 16.8 - In Exercises 1–8, find the divergence of the...Ch. 16.8 - Prob. 4ECh. 16.8 - Prob. 5ECh. 16.8 - Prob. 6ECh. 16.8 - Prob. 7ECh. 16.8 - In Exercises 1–8, find the divergence of the...Ch. 16.8 - Prob. 9ECh. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - Prob. 11ECh. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - Prob. 13ECh. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - Prob. 15ECh. 16.8 - Prob. 16ECh. 16.8 - Prob. 17ECh. 16.8 - Prob. 18ECh. 16.8 - Prob. 19ECh. 16.8 - Prob. 20ECh. 16.8 - Prob. 21ECh. 16.8 - Prob. 22ECh. 16.8 - Prob. 23ECh. 16.8 - Prob. 24ECh. 16.8 - Prob. 25ECh. 16.8 - Prob. 26ECh. 16.8 - Calculate the net outward flux of the vector...Ch. 16.8 - Prob. 28ECh. 16.8 - Prob. 29ECh. 16.8 - Prob. 30ECh. 16.8 - Prob. 31ECh. 16.8 - Prob. 32ECh. 16.8 - Prob. 33ECh. 16.8 - Green’s second formula (Continuation of Exercise...Ch. 16.8 - Prob. 35ECh. 16.8 - Prob. 36ECh. 16 - Prob. 1GYRCh. 16 - Prob. 2GYRCh. 16 - Prob. 3GYRCh. 16 - Prob. 4GYRCh. 16 - Prob. 5GYRCh. 16 - Prob. 6GYRCh. 16 - Prob. 7GYRCh. 16 - Prob. 8GYRCh. 16 - Prob. 9GYRCh. 16 - Prob. 10GYRCh. 16 - Prob. 11GYRCh. 16 - Prob. 12GYRCh. 16 - Prob. 13GYRCh. 16 - Prob. 14GYRCh. 16 - Prob. 15GYRCh. 16 - Prob. 16GYRCh. 16 - Prob. 17GYRCh. 16 - Prob. 18GYRCh. 16 - Prob. 1PECh. 16 - Prob. 2PECh. 16 - Prob. 3PECh. 16 - Prob. 4PECh. 16 - Prob. 5PECh. 16 - Prob. 6PECh. 16 - Prob. 7PECh. 16 - Prob. 8PECh. 16 - Prob. 9PECh. 16 - Prob. 10PECh. 16 - Prob. 11PECh. 16 - Area of a parabolic cap Find the area of the cap...Ch. 16 - Prob. 13PECh. 16 - Prob. 14PECh. 16 - Prob. 15PECh. 16 - Prob. 16PECh. 16 - Prob. 17PECh. 16 - Prob. 18PECh. 16 - Prob. 19PECh. 16 - Prob. 20PECh. 16 - Prob. 21PECh. 16 - Prob. 22PECh. 16 - Prob. 23PECh. 16 - Prob. 24PECh. 16 - Prob. 25PECh. 16 - Prob. 26PECh. 16 - Prob. 27PECh. 16 - Prob. 28PECh. 16 - Prob. 29PECh. 16 - Prob. 30PECh. 16 - Prob. 31PECh. 16 - Prob. 32PECh. 16 - Prob. 33PECh. 16 - Find potential functions for the fields in...Ch. 16 - Prob. 35PECh. 16 - Prob. 36PECh. 16 - Prob. 37PECh. 16 - Prob. 38PECh. 16 - Prob. 39PECh. 16 - Prob. 40PECh. 16 - Prob. 41PECh. 16 - Prob. 42PECh. 16 - Prob. 43PECh. 16 - Prob. 44PECh. 16 - Prob. 45PECh. 16 - Prob. 46PECh. 16 - Prob. 47PECh. 16 - Prob. 48PECh. 16 - Prob. 49PECh. 16 - Prob. 50PECh. 16 - Prob. 51PECh. 16 - Prob. 52PECh. 16 - Prob. 53PECh. 16 - Prob. 54PECh. 16 - Prob. 55PECh. 16 - Prob. 56PECh. 16 - Prob. 57PECh. 16 - Prob. 58PECh. 16 - Prob. 59PECh. 16 - Prob. 60PECh. 16 - Prob. 1AAECh. 16 - Prob. 2AAECh. 16 - Prob. 3AAECh. 16 - Prob. 4AAECh. 16 - Prob. 5AAECh. 16 - Prob. 6AAECh. 16 - Prob. 7AAECh. 16 - Find the mass of a helicoids
r(r, ) = (r cos )i +...Ch. 16 - Prob. 9AAECh. 16 - Prob. 10AAECh. 16 - Prob. 11AAECh. 16 - Prob. 12AAECh. 16 - Archimedes’ principle If an object such as a ball...Ch. 16 - Prob. 14AAECh. 16 - Prob. 15AAECh. 16 - Prob. 16AAECh. 16 - Prob. 17AAECh. 16 - Prob. 18AAECh. 16 - Prob. 19AAECh. 16 - Prob. 20AAECh. 16 - Prob. 21AAE
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