In each of Problems 47 and 48 , determine the values of α , if any, for which all solutions tend to zero as t → ∞ ; also determine the values of α , if any, for which all (nonzero) solutions become unbounded as t → ∞ . y ″ − ( 2 α − 3 ) y ′ + α ( α − 3 ) y = 0
In each of Problems 47 and 48 , determine the values of α , if any, for which all solutions tend to zero as t → ∞ ; also determine the values of α , if any, for which all (nonzero) solutions become unbounded as t → ∞ . y ″ − ( 2 α − 3 ) y ′ + α ( α − 3 ) y = 0
In each of Problems
47
and
48
, determine the values of
α
, if any, for which all solutions tend to zero as
t
→
∞
; also determine the values of
α
, if any, for which all (nonzero) solutions become unbounded as
t
→
∞
.
1. A telegraph can transmit two different signals: a dot and a dash. We want to encode the 26 letters of the English
alphabet and the ten digits 0, 1, 2, . . . , 9 using sequences of these two symbols. What is the smallest integer n such
that we can encode all these letters and digits with sequences of length at most n and length at least 1?
Use the graph of y = f(x) to answer the following.
3-
2
-4
-2
-1
1
2
3
4
-1
2
m
-3-
+
(d) Find all x for which f(x) = -2.
If there is more than one value, separate them with commas or write your answer in interval notation, if necessary. Select "None", if applicable.
Value(s) of x for which f(x)=-2: |
(0,0) (0,0) (0,0)
(0,0) 0,0...
-00
None
(h) Determine the range of f.
The range is
(0,0)
G
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A gardener has ten different potted plants, and they are spraying the plants with doses of
Tertizers. Plants can receive zero or more doses in a session. In the following, we count each
possible number of doses the ten plants can receive (the order of spraying in a session does
not matter).
(a) How many ways are there if there were twelve total doses of a single type of fertilizer?
(b) How many ways are there if there are six total doses of a single type of fertilizer, each
plant receives no more than one dose?
(c) How many ways are there if is was one dose of each of six types of fertilizers?
(d) How many ways are there if there are four doses of fertilizer #1 and eight doses of
fertilizer #2?
(e) How many ways are there if there are four doses of fertilizer #1 and eight doses of
fertilizer #2, and each plant receives no more than one dose of fertilizer #1?
(f) How many ways are there to do two sessions of spraying, where each plant receives at
most two doses total?
Chapter 4 Solutions
Differential Equations: An Introduction to Modern Methods and Applications
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