Exam 1 a
Show Work!!
1)(40 points) Compute the following limits
a
) lim
x
→∞
√
ln
x
x
b
) lim
x
→∞
x
1
√
x
c
) lim
x
→∞
xe
-
x
d
) lim
n
→∞
parenleftbigg
1
-
1
2
n
parenrightbigg
3
n
2)(60 points) Do the following converge or diverge? Why?
a
)
∞
summationdisplay
n
=1
(
-
1)
n
n
1
n
b
)
∞
summationdisplay
n
=1
1
n
3
n
+1
c
)
∞
summationdisplay
n
=1
n
2
+ 2
n
n
3
-
1
d
)
∞
summationdisplay
n
=1
1
n
2
+ 2
n
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%" -;4> ?7
4 5;9
9;#8:6 2;
:!
4=6
4 01>;9 ?
49#+ ,;:38?
8;:0
9
9
#+ /7
#+
!
#
!
$"
&
&
% $
&
" .
8:3 ?7
4 =038 > ;5 2;:!
4=6
4:2
4 ;5 ?7
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- Spring '10
- K.Davis
- Limits, Following, lim, Natural logarithm
-
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