Simplify each of the following as much as possible. For example,
O(3 a^ 2 + 2 a ) simplifies to O( a^ 2). ( Hint: A few are already as simple as possible.)
a. O(5)
b. O( log_(base 3) a )
c. O( log a + 1)
d. O( log a^ 2)
e. O(( log a )^2)
f. ( a + log a )
g. ( log a + 1)
h. (max( a^ 2, a ))
i. (2^ n + n^ 100)
j. ( a 2 + 2 a )
k. (3 n^ 2 + 2 n + log n + 1)
l. ( n 2^ n )
m. (3^ n + 2^ n )
Solution
a. O(1)
b. O(loga)

c. O(loga)
d. O(loga)
e. O((loga)^2)
f. (a)
g. (loga)
h. (a^2)
i. (n^100)
j. (a^2)
k. (n^2)
l. (n2^n)
m. (3^n)