Victor Chamacho
Assignment HW1 Limits I due 01/19/2012 at 11:00pm MST
5. (1 pt) Library/ma123DB/set10/s11 1 17.pg
n2 +2n+4
Find the limit of the sequence: an = 2n
2 +2n+6
1. (1 pt) Library/UMN/calculusStewartCCC/s 11 1 4.pg
List the first five terms of the sequence:
an =
a1 =
, a2 =
n+3
.
3n − 1
, a3 =
Answer:
, a4 =
6. (1 pt) Library/ma123DB/set10/s11 1 36.pg
Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit.
, and a5 =
2. (1 pt) Library/ma123DB/set10/s11 1 9.pg
For each sequence, find a formula for the general term, an . For
example, answer n2 if given the sequence {1, 4, 9, 16, 25, 36, ...}
1.
2.
1
2,
1
2,
1
4,
1
4,
1
8,
1
6,
math1210spring2012-3
(If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it
diverges without being infinity or negative infinity, state your
answer as div )
1
16 , ...
1
8 , ...
−8n6 + sin2 (5n)
n→∞
n6 + 6
3. (1 pt) Library/ma123DB/set10/s11 1 32.pg
Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit.
lim
Answer:
7. (1 pt) Library/ma123DB/set10/s11 1 16.pg
7n−6
Find the limit of the sequence: an = 7n+7
(If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it
diverges without being infinity or negative infinity, state your
answer as div )
Answer:
8. (1 pt) Library/OSU/accelerated calculus and analytic geometry ii/hmwk1/prob16.pg
Determine whether the sequences are increasing, decreasing, or
not monotonic. If increasing, enter 1 as your answer. If decreasing, enter -1 as your answer. If not monotonic, enter 0 as your
answer.
lim [ln(n + 1) − ln(n)]
n→∞
Answer:
1. an =
2. an =
4. (1 pt) Library/ma123DB/set10/s11 1 19.pg
Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit.
3. an =
4. an =
(If it diverges to infinity, state your answer as inf . If it
diverges to negative infinity, state your answer as -inf . If it
diverges without being infinity or negative infinity, state your
answer as div .)
1
4n+8
cos n
n
√4
n+4
8n+4
n−4
n+4
10. (1 pt) Library/ma123DB/set10/s11 1 28.pg
Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit.
(If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it
diverges without being infinity or negative infinity, state your
answer as div )
13(4n ) + 11
n→∞
9(2n )
lim
Answer:
lim (−1)n sin(13/n)
n→∞
1
diverges without being infinity or negative infinity, state your
answer as ”DIV”.
Answer:
11. (1 pt) Library/maCalcDB/setSequences2Limits/ur sq 2 17.pg
Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit. If it diverges to infinity, state
your answer as ”INF” (without the quotation marks). If it diverges to negative infinity, state your answer as ”MINF”. If it
lim
n3
n→∞ e−6n
c
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