Dwnload Full Calculus Early Transcendentals 7th Edition Edwards Solutions Manual PDF
Dwnload Full Calculus Early Transcendentals 7th Edition Edwards Solutions Manual PDF
Dwnload Full Calculus Early Transcendentals 7th Edition Edwards Solutions Manual PDF
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-solutions-manual/
Section 3.1
3.1.2: Given g(t) = −16t2 + 100, we have a = −16, b = 0, and c = 100, so g (t) = 2at + b = −32t.
3.1.3: If h(z) = z(25 − z) = −z 2 + 25z, then a = −1, b = 25, and c = 0, so h (z) = 2az + b = −2z + 25.
3.1.4: If f (x) = −49x + 16, then a = 0, b = −49, and c = 16, so f (x) = −49.
dy
3.1.5: If y = 2x2 + 3x − 17, then a = 2, b = 3, and c = −17, so = 2ax + b = 4x + 3.
dx
dx
3.1.6: If x = −100t2 + 16t, then a = −100, b = 16, and c = 0, so = 2at + b = −200t + 16.
dt
dz
3.1.7: If z = 5u2 − 3u, then a = 5, b = −3, and c = 0, so = 2au + b = 10u − 3.
du
dv
3.1.8: If v = −5y 2 + 500y, then a = −5, b = 500, and c = 0, so = 2ay + b = −10y + 500.
dy
dx
3.1.9: If x = −5y 2 + 17y + 300, then a = −5, b = 17, and c = 300, so = 2ay + b = −10y + 17.
dy
du
3.1.10: If u = 7t2 + 13t, then a = 7, b = 13, and c = 0, so = 2at + b = 14t + 13.
dt
1 1
−
f (x + h) − f (x) 2(x + h) + 1 2x +1
3.1.15: f (x) = lim = lim
h→0 h h→0 h
112
1 1
−
f (x + h) − f (x) 3 − (x + h) 3 − x
3.1.16: f (x) = lim = lim
h→0 h h→0 h
(3 − x) − (3 − x − h) 3−x−3+x+h h
= lim = lim = lim
h→0 h(3 − x − h)(3 − x) h→0 h(3 − x − h)(3 − x) h→0 h(3 − x − h)(3 − x)
1 1
= lim = .
h→0 (3 − x − h)(3 − x) (3 − x)2
√
f (x + h) − f (x) 2(x + h) + 1 − 2x + 1
3.1.17: f (x) = lim = lim
h→0 h h→0 h
√ √ √ √
2x + 2h + 1 − 2x + 1 2x + 2h + 1 + 2x + 1
= lim √ √
h→0 h 2x + 2h + 1 + 2x + 1
(2h + 2h + 1) − (2x + 1)
= lim √ √
h→0 h 2x + 2h + 1 + 2x + 1
2h 2
= lim √ √ = lim √ √
h→0 h 2x + 2h + 1 + 2x + 1 h→0 2x + 2h + 1 + 2x + 1
2 1
= √ = √ .
2 2x + 1 2x + 1
1 1 1 1
3.1.18: f (x) = lim
(f (x + h) − f (x)) = lim √ −√
h→0 h h→0 h x+h+1 x+1
√ √ √ √ √ √
x+1− x+h+1 x+1− x+h+1 x+1+ x+h+1
= lim √ √ = lim √ √ √ √
h→0 h x + h + 1 x + 1 h→0 h x+h+1 x+1 x+1+ x+h+1
(x + 1) − (x + h + 1)
= lim √ √ √ √
h→0 h x+h+1 x+1 x+1+ x+h+1
−h
= lim √ √ √ √
h→0 h x+h+1 x+1 x+1+ x+h+1
−1
= lim √ √ √ √
h→0 x+h+1 x+1 x+1+ x+h+1
−1 1
= √ 2 √ =− .
x+1 2 x+1 2(x + 1)3/2
1 1 x+h x
3.1.19: f (x) = lim (f (x + h) − f (x)) = lim −
h→0 h h→0 h 1 − 2(x + h) 1 − 2x
1 (x + h)(1 − 2x) − (1 − 2x − 2h)(x) (x − 2x2 + h − 2xh) − (x − 2x2 − 2xh)
= lim · = lim
h→0 h (1 − 2x − 2h)(1 − 2x) h→0 h(1 − 2x − 2h)(1 − 2x)
x − 2x2 + h − 2xh − x + 2x2 + 2xh h
= lim = lim
h→0 h(1 − 2x − 2h)(1 − 2x) h→0 h(1 − 2x − 2h)(1 − 2x)
1 1
= lim = .
h→0 (1 − 2x − 2h)(1 − 2x) (1 − 2x)2
113
−2 2
= lim =− .
h→0 (x + h − 1)(x − 1) (x − 1)2
dx
3.1.21: The velocity of the particle at time t is = v(t) = −32t, so v(t) = 0 when t = 0. The position of
dt
the particle then is x(0) = 100.
dx
3.1.22: The velocity of the particle at time t is = v(t) = −32t + 160, so v(t) = 0 when t = 5. The
dt
position of the particle then is x(5) = 425.
dx
3.1.23: The velocity of the particle at time t is = v(t) = −32t + 80, so v(t) = 0 when t = 2.5. The
dt
position of the particle then is x(2.5) = 99.
dx
3.1.24: The velocity of the particle at time t is = v(t) = 200t, so v(t) = 0 when t = 0. The position of
dt
the particle then is x(0) = 50.
dx
3.1.25: The velocity of the particle at time t is = v(t) = −20 − 10t, so v(t) = 0 when t = −2. The
dt
position of the particle then is x(−2) = 120.
dy
3.1.26: The ball reaches its maximum height when its velocity v(t) = = −32t + 160 is zero, and v(t) = 0
dt
when t = 5. The height of the ball then is y(5) = 400 (ft).
dy
3.1.27: The ball reaches its maximum height when its velocity v(t) = = −32t + 64 is zero, and v(t) = 0
dt
when t = 2. The height of the ball then is y(2) = 64 (ft).
dy
3.1.28: The ball reaches its maximum height when its velocity v(t) = = −32t + 128 is zero, and v(t) = 0
dt
when t = 4. The height of the ball then is y(4) = 281 (ft).
dy
3.1.29: The ball reaches its maximum height when its velocity v(t) = = −32t + 96 is zero, and v(t) = 0
dt
when t = 3. The height of the ball then is y(3) = 194 (ft).
3.1.30: Figure 3.1.22 shows a graph first increasing, then with a horizontal tangent at x = 0, then decreasing.
Hence its derivative must be first positive, then zero when x = 0, then negative. This matches Fig. 3.1.28(c).
114
Language: English
[Contents]
THE GODS of
MEXICO
[Contents]
NEPHRITE FIGURE OF A DEATH-GOD.
[Frontispiece
[Contents]
THE
GODS OF MEXICO
By LEWIS SPENCE
FELLOW OF THE ROYAL
ANTHROPOLOGICAL
INSTITUTE OF GREAT BRITAIN AND
IRELAND
ILLUSTRATED
NEW YORK
FREDERICK A. STOKES COMPANY
PUBLISHERS
1923
[Contents]
TO
MY WIFE,
WITH DEEPEST GRATITUDE
AND AFFECTION
[Contents]
This book deals exclusively with the religion of the peoples of ancient
Mexico. With the history and archæology of that country I am not
concerned in these pages, unless where they have a bearing upon
the main subject. By “Mexico” I mean that region of North America
lying between the Tropic of Cancer and the Isthmus of Tehuantepec.
Thus only passing reference to the religion of the Maya of Yucatan or
the Quiche of Guatemala is made in the way of occasional
comparison.
I have thought it best at the outset to make these points clear beyond
the possibility of misapprehension. It was formerly usual to regard the
entire tract occupied by Central American civilization from the Tropic
of Cancer to Nicaragua as one and indivisible in its manifestations.
But it is now clear that the type of advancement peculiar to the more
northerly portion inhabited by the Nahua (Aztec and Chichimec)
peoples of Mexico proper presents numerous and striking
divergencies from the more southerly though related Maya civilization
of Yucatan and Guatemala. Regarding the priority of these two
cultures no doubt exists. The Maya was greatly the more ancient. But
during the century preceding the conquest of Mexico by Cortéz it had
been subjected to Nahua immigration and influences, especially as
regards its religious beliefs. It is therefore necessary to exercise
caution in the identification of Nahua or Mexican with Maya myths
and divine forms, and with this in view I have directed my researches
more especially to an examination of the deities and ritual practices
of the Mexican area, in the hope that once the fundamental beliefs of
this better-known [vi]region have been ascertained, the results arrived
at may be applied with some measure of confidence to the obscure
field of Maya belief. It seemed to me also essential, if progress were
to be made, to apply a more intensive method of investigation than
has hitherto been deemed possible or desirable to the first origins of
the Mexican gods, and it is especially with the results obtained by
this means that I am concerned rather than with the conclusions of
others.
I have chosen The Gods of Mexico as the title of this book, as its
contents refer more particularly to the development and general
description of the deities of ancient Anahuac than to the questions of
ritual, priesthood, or religious architecture. It has seemed to me that,
once the fundamental nature of the gods has been made clear, when
the multitudinous and conflicting details regarding them have been
sifted, collated, and reduced to order, more will have been done to
discover the whole purport of Mexican religion than if investigation
had been directed in particular to ritual practice. But that I have not
neglected the question of ritual is proved by the extended notices of
the festivals I have appended to the description of each of the gods. I
have, however, confined my descriptions and criticisms of ceremonial
to these, and have refrained from the illustration of the sacraments of
life and death, baptism, burial, and the like, as it is my hope to be
able to deal with the whole subject of ritualistic practice among the
Mexicans at a future date.
The illustrations in this book are, for the most part, taken from the
native Mexican codices or paintings, and from representations of the
gods in stone or pottery. It has, of course, been impossible to furnish
every picture or representation alluded to in the text, but these, in
their entirety, will be found in the excellent coloured reproductions in
collotype published by the Duc de Loubat, full particulars of which are
given in the bibliography of the codices on pages 378–381. These
reproductions can be consulted in many of the greater libraries,
especially in those connected with the Universities. I have preferred,
in many cases, to furnish the student with those representations of
the gods which he would have found it more or less difficult to
procure. The numbers of the pages or sheets attached to the
illustrations refer to the places where the respective figures can be
found in the reproductions of the Duc de Loubat.
1 See Bibliography for description of this and all other works alluded to throughout
the work. ↑
[Contents]
CONTENTS
CHAPTER I
INTRODUCTORY
CHAPTER II
COSMOGONY
CHAPTER III
THE GREAT GODS
Method of treatment—Uitzilopochtli—Tezcatlipocâ—Quetzalcoatl
pp. 65–145
CHAPTER IV
CHAPTER V
Introductory—Tlazolteotl—Chicomecoatl—Cinteotl—Ciuacoatl—
Coatlicue—Xochiquetzal—Macuilxochitl or Xochipilli—Xipe—
Xilonen—Itzpapalotl—Zapotlantenan—Ilamatecutli pp. 153–
233
CHAPTER VI
Introductory—Tlaloc—Chalchihuitlicue—Uixtociuatl—Atlaua—
Napatecutli—Matlalcuêyê—Opochtli pp. 234–267
CHAPTER VII
THE FIRE-GODS
General—Tezcatzoncatl—Tepoxtecatl—Patecatl—Mayauel—
Totoltecatl—Macuiltochtli—Totochtin—Tomiauhtecutli pp.
285–299
CHAPTER IX
CHAPTER X
CHAPTER XI
CHAPTER XII
MINOR DEITIES
Xolotl—Ixtlilton—Omacatl—The Ciuateteô or Ciuapipiltin pp.
344–358
APPENDIX
[Contents]
ILLUSTRATIONS
[xvi]
[Contents]
NOTE ON THE PRONUNCIATION OF MEXICAN
Uitzilopochtli = Wit-zil-o-potchtly
Tezcatlipocâ = Tez-catly-pocā
Quetzalcoatl = Quetzal-co-at-ly
Xipe = Shee-pay
Chalchihuitlicue = Chal-chĕĕ-wĕĕt-lēē-kway.
[Contents]
If, like the necromancers of old, we possessed the power to summon the shades of
the dead before us, and employed this dread authority to recall from the place of
shadows the spirit of a member of the priesthood of ancient Mexico, in order that
we might obtain from him an account of the faith which he had professed while in
the body, it is improbable that we would derive much information regarding the
precise significance of the cult of which he was formerly an adherent without
tedious and skilful questioning. He would certainly be able to enlighten us readily
enough on matters of ritual and mythology, calendric science and the like; but if we
were to press him for information regarding the motives underlying the outer
manifestations of his belief, he would almost certainly disappoint us, unless our
questionary was framed in the most careful manner. In all likelihood he would be
unable to comprehend the term “religion,” of which we should necessarily have to
make use, and which it would seem so natural for us to employ; and he would
scarcely be capable of dissociating the circumstances of his faith from those of
Mexican life in general, especially as regards its political, military, agricultural, and
artistic connections.
Nor would he regard magic or primitive science as in any way alien to the activities
of his office. But if we became more importunate, and begged him to make some
definite statement regarding the true meaning and import of his [2]religion ere he
returned to his place, he might, perhaps, reply: “If we had not worshipped the gods
and sacrificed to them, nourished them with blood and pleasured them with gifts,
they would have ceased to watch over our welfare, and would have withheld the
maize and water which kept us in life. The rain would not have fallen and the crops
would not have come to fruition.” 1 If he employed some such terms as these, our
phantom would outline the whole purport of the system which we call Mexican
religion, the rude platform on which was raised the towering superstructure of rite
and ceremony, morality and tradition, a part of which we are about to examine.
The writer who undertakes the description of any of the great faiths of the world
usually presupposes in his readers a certain acquaintance with the history and
conditions of the people of whose religion he treats. But the obscurity which
surrounded all questions relating to Mexican antiquity until the beginning of this
century formerly made it essential that any view of its religious phase should be
prefaced by an account of the peoples who professed it, their racial affinities, and
the country they occupied. This necessity no longer exists. The ground has been
traversed so often of late, and I have covered it so frequently in previous works, 2
that I feel only a brief account of these conditions is necessary here, such, in a
word, as will enable the reader to realize circumstances of race, locality, and
period.
The people whose religious ideas this book attempts to describe were the Nahua
of pre-Colombian Mexico, a race by no means extinct, despite the oft-repeated
assertions of popular novelists, and which is now usually classed as a branch of
the great Uto-Aztecan family of the North American Indian stock. They spoke, and
their descendants still speak, a language known as the Nahuatl, or Nahuatlatolli
(“speech of those who live by rule” or “by ritual observance”). At the era of the
Spanish invasion of their country in 1519 [3]they had succeeded in overrunning and
reducing to their dominion practically all that part of modern Mexico which lies
between the Tropic of Cancer and the Isthmus of Tehuantepec. They were, in all
probability, immigrants from the north, and their art-forms, no less than their
physique and beliefs, have led certain writers to form the opinion that they came
originally from the neighbourhood of British Columbia, or that they had a common
origin with the Indian tribes which inhabit that region at the present time.
However this may be, the first Nahua immigrants would appear to have entered
the Valley of Mexico at some time during the eighth century of our era. But the
Aztecâ, part of a later swarm of Nahua, do not seem to have descended upon it
until the middle of the thirteenth century, or to have founded the settlement of
Mexico-Tenochtitlan until about the year 1376. At the period of their arrival in the
valley they were a barbarous tribe of nomadic hunters, wandering from place to
place in search of fresh hunting-grounds, precisely as did many North American
Indian tribes before reservations were provided for them. Gradually, by virtue of
their superior prowess in war, they achieved the hegemony of the Plateau of
Anahuac, which boasted a tradition and civilization at least five hundred years old.
These they proceeded to assimilate with marvellous rapidity, as is not infrequently
the case when a race of hunters mingles with a settled agricultural population.
Indeed, in the course of the century and a quarter which intervened between the
founding of Mexico and the period of the Spanish Conquest, they had arrived at
such a standard of civilization as surprised their Castilian conquerors. When the
Aztecâ, abandoning their wandering life, finally settled in the Valley of Anahuac,