Biocalculus: Calculus For Life Sciences
15th Edition
ISBN: 9781305177291
Author: James Stewart, Troy Day
Publisher: Cengage Learning
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Chapter 10, Problem 1CC
To determine
To State:The difference between autonomous and non-autonomous system of
Expert Solution & Answer
Explanation of Solution
A system of differential equations is called autonomous system of differential equations, if the equations do not explicitly contain the independent variable.
A system of differential equations is called as non-autonomous system of differential equations, if the equations depend on the independent variable expicitely.
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(3) (20 points) Let F(x, y, z) = (y, z, x²z). Define
E = {(x, y, z) | x² + y² ≤ z ≤ 1, x ≤ 0}.
(a) (2 points) Calculate the divergence V. F.
(b) (4 points) Let D = {(x, y) | x² + y² ≤ 1, x ≤ 0} Without calculation, show that
the triple integral
√ (V · F) dV = √ 2²(1.
= x²(1 − x² - y²) dA.
E
(2) (22 points) Let F(x, y, z) = (x sin y, cos y, ―xy).
(a) (2 points) Calculate V. F.
(b) (6 points) Given a vector field
is everywhere defined with V
G₁(x, y, z) = *
G2(x, y, z) = −
G3(x, y, z) = 0.
0
0
F(x, y, z) = (F₁(x, y, z), F₂(x, y, z), F(x, y, z)) that
F = 0, let G = (G1, G2, G3) where
F₂(x,
y,
y, t) dt
- √ F³(x, t, 0) dt,
*
F1(x,
y, t) dt,
t) dt - √ F
Calculate G for the vector field F(x, y, z) = (x sin y, cos y, -xy).
Evaluate the following integral over the Region R.
(Answer accurate to 2 decimal places).
√ √(x + y) A
R
R = {(x, y) | 25 < x² + y² ≤ 36, x < 0}
Hint: The integral and Region is defined in rectangular coordinates.
Chapter 10 Solutions
Biocalculus: Calculus For Life Sciences
Ch. 10.1 - Prob. 12ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 9ECh. 10.4 - Prob. 1ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 15E
Ch. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10 - Prob. 1CCCh. 10 - Prob. 2CCCh. 10 - Prob. 3CCCh. 10 - Prob. 4CCCh. 10 - Prob. 3TFQCh. 10 - Prob. 1ECh. 10 - Prob. 2ECh. 10 - Prob. 3ECh. 10 - Prob. 4ECh. 10 - Prob. 5ECh. 10 - Prob. 6ECh. 10 - Prob. 7ECh. 10 - Prob. 14ECh. 10 - Prob. 15ECh. 10 - Prob. 16ECh. 10 - Prob. 17ECh. 10 - Prob. 27ECh. 10 - Prob. 28ECh. 10 - Prob. 29E
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