Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 5.2, Problem 18PS
To determine
To evaluate: The given limit.
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Students have asked these similar questions
Problem 5.
Prove the following three statements:
(a) Any convergent sequence (xn) is bounded.
(b) Let (xn) and (yn) be two convergent sequences, and suppose that their limits
→ M. Show that the sequence (xn + Yn), obtained by
are xn
→ L and Yn
summing them termwise, is a convergent sequence, and in fact
Xn + Yn
→ (L+ M).
(c) There exist bounded sequences which are not convergent.
Problem 2.
Consider the following four sequences of real numbers:
2n + 1
1
n!
3n?
1
Yn =
n!
Wn
Зп — 4'
nn'
n2 +n
In this exercise, you must use the e-definition of the limit (Definition in Section 10.4)
to show the following statements.
(a) Show that lim xn = 2/3,
(b) Show that lim yn = 0,
(c) Show that lim zn = 0,
(d) Show that lim wn = 3.
In each of these four cases above, you must write a complete detailed and self-contained
proof that the limit is the one stated. Each can be done directly from the definition.
Be clear in the use of ɛ, the quantifiers and the indices when you write the four proofs
above. In particular, write clearly what you are given and what you must prove when
writing down the definition of each of the limits.
6.
B3.3.4.1f) (1) Use limit laws and SL. 1 - SL. 8 for sequences, to evaluate the following limits:
- n! +4¹/n
2ne2n
lim
81x
COS N-
Chapter 5 Solutions
Calculus
Ch. 5.1 - Prob. 1PSCh. 5.1 - Prob. 2PSCh. 5.1 - Prob. 3PSCh. 5.1 - Prob. 4PSCh. 5.1 - Prob. 5PSCh. 5.1 - Prob. 6PSCh. 5.1 - Prob. 7PSCh. 5.1 - Prob. 8PSCh. 5.1 - Prob. 9PSCh. 5.1 - Prob. 10PS
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