University Calculus: Early Transcendentals, Loose-leaf Edition (4th Edition)
4th Edition
ISBN: 9780135164860
Author: Joel R. Hass, Christopher Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Chapter 16.5, Problem 4E
To determine
The ways in which the competitive hunters model be validated; discuss about the estimation of various constants
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Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
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Chapter 16 Solutions
University Calculus: Early Transcendentals, Loose-leaf Edition (4th Edition)
Ch. 16.1 - In Exercises 1–4, match the differential equations...Ch. 16.1 - In Exercises 1–4, match the differential equations...Ch. 16.1 - In Exercises 1–4, match the differential equations...Ch. 16.1 - In Exercises 1–4, match the differential equations...Ch. 16.1 - In Exercises 5 and 6, copy the slope fields, and...Ch. 16.1 - In Exercises 5 and 6, copy the slope fields, and...Ch. 16.1 - Prob. 7ECh. 16.1 - Prob. 8ECh. 16.1 - Prob. 9ECh. 16.1 - Prob. 10E
Ch. 16.1 - Prob. 11ECh. 16.1 - Prob. 12ECh. 16.1 - Prob. 13ECh. 16.1 - Prob. 14ECh. 16.1 - In Exercises 15–20, use Euler’s method to...Ch. 16.1 - In Exercises 15–20, use Euler’s method to...Ch. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Prob. 19ECh. 16.1 - Prob. 20ECh. 16.1 - Prob. 21ECh. 16.1 - Prob. 22ECh. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Prob. 26ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 4ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 6ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 8ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 10ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 12ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 14ECh. 16.2 - Solve the initial value problems in Exercises...Ch. 16.2 - Prob. 16ECh. 16.2 - Solve the initial value problems in Exercises...Ch. 16.2 - Prob. 18ECh. 16.2 - Solve the initial value problems in Exercises...Ch. 16.2 - Prob. 20ECh. 16.2 - Solve the exponential growth/decay initial value...Ch. 16.2 - Solve the following initial value problem for u as...Ch. 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 - Solve the Bernoulli equations in Exercises...Ch. 16.2 - Solve the Bernoulli equations in Exercises...Ch. 16.2 - Solve the Bernoulli equations in Exercises...Ch. 16.2 - Solve the Bernoulli equations in Exercises...Ch. 16.3 - Coasting bicycle A 66-kg cyclist on a 7-kg bicycle...Ch. 16.3 - Coasting battleship Suppose that an Iowa class...Ch. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.3 - Prob. 10ECh. 16.3 - Prob. 11ECh. 16.3 - Find the family of solutions of the given...Ch. 16.3 - Salt mixture A tank initially contains 100 gal of...Ch. 16.3 - Mixture problem A 200-gal is half full of...Ch. 16.3 - Fertilizer mixture A tank contains 100 gal of...Ch. 16.3 - Carbon monoxide pollution An executive conference...Ch. 16.4 - Prob. 1ECh. 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 - Prob. 8ECh. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - Prob. 14ECh. 16.4 - Prob. 15ECh. 16.4 - Prob. 16ECh. 16.4 - Prob. 17ECh. 16.4 - The spread of information Sociologists recognize a...Ch. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16.5 - Prob. 3ECh. 16.5 - Prob. 4ECh. 16.5 - Consider another competitive-hunter model defined...Ch. 16.5 - Prob. 6ECh. 16.5 - Two trajectories approach equilibrium Show that...Ch. 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 - Prob. 1GYRCh. 16 - What is a general solution? What is a particular...Ch. 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. 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 - Prob. 12PECh. 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. 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. 1AAECh. 16 - Prob. 2AAECh. 16 - Prob. 3AAECh. 16 - Prob. 4AAECh. 16 - Solve the homogeneous equations in Exercises 5–10....Ch. 16 - Prob. 6AAECh. 16 - Prob. 7AAECh. 16 - Prob. 8AAECh. 16 - Prob. 9AAECh. 16 - Prob. 10AAE
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