Precalculus: A Unit Circle Approach
2nd Edition
ISBN: 9780321825391
Author: Ratti
Publisher: PEARSON
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Textbook Question
Chapter A.2, Problem 62E
In Exercises 61-108, factor each polynomial completely. If a polynomial cannot be factorized, state that it is irreducible.
62.
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Find the limit. (If the limit is infinite, enter 'oo' or '-o', as appropriate. If the limit does not otherwise exist, enter DNE.)
lim
X→ ∞
(✓
81x2
-
81x + x
9x)
2) Compute the following anti-derivative.
√1x4 dx
Question 3 (5pt): A chemical reaction. In an elementary chemical reaction,
single molecules of two reactants A and B form a molecule of the product C :
ABC. The law of mass action states that the rate of reaction is proportional
to the product of the concentrations of A and B:
d[C]
dt
= k[A][B]
(where k is a constant positive number). Thus, if the initial concentrations are
[A] =
= a moles/L and [B] = b moles/L we write x = [C], then we have
(E):
dx
dt
=
k(ax)(b-x)
1
(a) Write the differential equation (E) with separate variables, i.e. of the form
f(x)dx = g(t)dt.
(b) Assume first that a b. Show that
1
1
1
1
=
(a - x) (b - x)
-
a) a - x
b - x
b)
(c) Find an antiderivative for the function f(x) = (a-x) (b-x) using the previous
question.
(d) Solve the differentiel equation (E), i.e. find x as a function of t. Use the fact
that the initial concentration of C is 0.
(e) Now assume that a = b. Find x(t) assuming that a = b. How does this
expression for x(t) simplify if it is known that [C] =…
Chapter A.2 Solutions
Precalculus: A Unit Circle Approach
Ch. A.2 - In Exercises 1-4, determine whether the given...Ch. A.2 - In Exercises 1-4, determine whether the given...Ch. A.2 - In Exercises 1-4, determine whether the given...Ch. A.2 - Prob. 4ECh. A.2 - In Exercises 5-8, find the degree and list the...Ch. A.2 - Prob. 6ECh. A.2 - Prob. 7ECh. A.2 - Prob. 8ECh. A.2 - In Exercises 9-16, perform the indicated...Ch. A.2 - In Exercises 9-16, perform the indicated...
Ch. A.2 - In Exercises 9-16, perform the indicated...Ch. A.2 - Prob. 12ECh. A.2 - Prob. 13ECh. A.2 - Prob. 14ECh. A.2 - Prob. 15ECh. A.2 - Prob. 16ECh. A.2 - Prob. 17ECh. A.2 - Prob. 18ECh. A.2 - Prob. 19ECh. A.2 - Prob. 20ECh. A.2 - Prob. 21ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 23ECh. A.2 - Prob. 24ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 26ECh. A.2 - Prob. 27ECh. A.2 - Prob. 28ECh. A.2 - Prob. 29ECh. A.2 - Prob. 30ECh. A.2 - Prob. 31ECh. A.2 - Prob. 32ECh. A.2 - Prob. 33ECh. A.2 - Prob. 34ECh. A.2 - Prob. 35ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 37ECh. A.2 - Prob. 38ECh. A.2 - Prob. 39ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 41ECh. A.2 - Prob. 42ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 46ECh. A.2 - Prob. 47ECh. A.2 - Prob. 48ECh. A.2 - Prob. 49ECh. A.2 - Prob. 50ECh. A.2 - Prob. 51ECh. A.2 - Prob. 52ECh. A.2 - Prob. 53ECh. A.2 - Prob. 54ECh. A.2 - Prob. 55ECh. A.2 - Prob. 56ECh. A.2 - Prob. 57ECh. A.2 - Prob. 58ECh. A.2 - Prob. 59ECh. A.2 - Prob. 60ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 66ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 68ECh. A.2 - Prob. 69ECh. A.2 - Prob. 70ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 75ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 81ECh. A.2 - Prob. 82ECh. A.2 - Prob. 83ECh. A.2 - Prob. 84ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 86ECh. A.2 - Prob. 87ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 94ECh. A.2 - Prob. 95ECh. A.2 - Prob. 96ECh. A.2 - Prob. 97ECh. A.2 - Prob. 98ECh. A.2 - Prob. 99ECh. A.2 - Prob. 100ECh. A.2 - Prob. 101ECh. A.2 - Prob. 102ECh. A.2 - Prob. 103ECh. A.2 - Prob. 104ECh. A.2 - Prob. 105ECh. A.2 - Prob. 106ECh. A.2 - Prob. 107ECh. A.2 - Prob. 108ECh. A.2 - Prob. 109ECh. A.2 - Prob. 110ECh. A.2 - Prob. 111ECh. A.2 - Prob. 112ECh. A.2 - Prob. 113ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 116ECh. A.2 - Prob. 117ECh. A.2 - Prob. 118ECh. A.2 - Prob. 119ECh. A.2 - Prob. 120ECh. A.2 - Prob. 121ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 123ECh. A.2 - Prob. 124ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 126ECh. A.2 - Prob. 127ECh. A.2 - Prob. 128ECh. A.2 - Prob. 129ECh. A.2 - Prob. 130ECh. A.2 - Prob. 131ECh. A.2 - Prob. 132ECh. A.2 - Prob. 133ECh. A.2 - Prob. 134ECh. A.2 - Prob. 135ECh. A.2 - Prob. 136ECh. A.2 - Prob. 137ECh. A.2 - Prob. 138ECh. A.2 - Prob. 139ECh. A.2 - Prob. 140ECh. A.2 - Prob. 141ECh. A.2 - Prob. 142ECh. A.2 - Prob. 143ECh. A.2 - Prob. 144E
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