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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
110. Let a
n
=
1
n
3
+ 1

n=1
. Then lim
n
a
n
= 0.
111. Let f ðxÞ= 15x + 7. Then lim
x2
f ðxÞ= 37.
112. Let f ðxÞ= x + 1
p
. Then lim
x3
f ðxÞ= 2. (Hint: Use, in a suit able way, the conjugate of x + 1
p
2.)
113. Let f ðxÞ= jxj. Then lim
x0
f ðxÞ= 0.
114. Let f ðxÞ=
x 3
x
2
9
. Then lim
x3
f ðxÞ= 1/6.
115. Let f ðxÞ=
x 3
x
2
9
. Then lim
x3
f ðxÞ does not exist.
Cardinality and Sizes of Infinity
116. The set A = fx jx ≥−10g is countable.
117. The inte rval (2, 10) is uncountable.
118. The set of irrational numbers in the interval (0, 1) is uncountable.
119. Consider the family fA
n
with n g of countable sets. For every k 2thesetA
1
× A
2
×
::::
× A
k
is
countable.
120. ...
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Publisher Resources

ISBN: 9780123822178