prob10 - n  n 1 Taylor Polynomials In problems 1 4 a...

Math 151 Spring 2008
Problem Set # 10
Sequences and Taylor Polynomials
Starred Problems will be turned in on Monday, April 7
Sequences
In problems 1-4 list the fi rst 4 terms of the sequence { a
n
} .
1.
a
n
= 2 n − 1 , n = 1 , 2 , 3 , . . .
2.
a
n
=
n
n 2 − 1
, n = 2 , 3 , 4 , . . .
3*.
a
n
= ( − 1)
n
1
3 n
, n = 0 , 1 , 2 , . . .
4*.
a
n
=
n
2
sin
³
(2 n + 1)
π
2
´
, n = 1 , 2 , 3 , . . .
In problems 5-21, determine the fi nite or in fi nite limit, if such a limit exists. You need to display
the steps that lead to your response, and provide an explanation if you claim that the limit does
not exist.
5.
lim
n →∞
5 n
2
+ 9
2 n 2 + 1
6*.
lim
n →∞
n
2
+ 10
4 n 3 + 1
7.
lim
n →∞
s
3 n 2
9 n 2 − 2
8*.
lim
n →∞
cos ( πn )
9.
lim
n →∞
sin
μ
πn
6 n + 2
¶
10*.
lim
n →∞
( − 1)
n
n
n + 4
11.
lim
n →∞
( − 1)
n
n
n 2 + 4
12*.
lim
n →∞
μ
−
3
4
¶
n
13.
lim
n →∞
μ
5
3
¶
n
14*.
lim
n →∞
n 3 − 1
2 n + 100
15*.
lim
n →∞
μ
−
3
2
¶
n
16.
lim
n →∞
e n
n
17*.
lim
n →∞
n
2
e
− n
18*.
lim
n →∞
n
2
10 n
19*.
lim
n →∞
ln ( n )
√
n
20.
lim
n →∞
n
1 / 3
log
10
( n )
21*.
lim
n →∞
μ
1 +