CS173: Discrete Mathematical Structures
Spring 2006
Homework #5
Due 02/19/06
1. For this problem, please log in to compass and answer the 5 true/false questions
contained in Quiz 1.
2. Consider the four following functions: f(x)
=
lne(lne(x)) , g(x)=ex,h(x)=x5,
t(x)=x10 . Find the domain of definition and the big-O of the following
functions:
a.
(fogoh)(x)
b.
(f−1og)(x)
c.
(g−1oh)(x)
d.
g(x) *[( fot−1)(x)]
3.
a. Evaluate: (j+1)2
(2i−1)
j=2
5−i
∑
i=1
4
∑
b. Let f(x) be the set of all even numbers smaller or equal than x. For
example, f(10)={0,2,4,6,8,10}. Let g(x)=2x.
Compute:
j
j∈(fog)(i)
∑
i=1
4
∑
c. There is also a special notation for products: an
i=1
n
∏=a1*a2*... * an.
Compute: −1
( )i2
i=5
10
∏
d. Express this sum in terms of n: 1
j−1
j+1
j=1
n
∑
e. Express this sum in terms of n: i
i=1
k
∑
k=1
n
∑
f. Express n! using product
∏
(
)
notation.
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