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Calculus Examples
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Calculus
Evaluate Using the Squeeze Theorem limit as x approaches infinity of arctan(e^x)
lim
x
→
∞
arctan
(
e
x
)
lim
x
→
∞
arctan
(
e
x
)
Step 1
Since the
exponent
x
x
approaches
∞
∞
, the
quantity
e
x
e
x
approaches
∞
∞
.
∞
∞
Step 2
Substitute
t
t
for
e
x
e
x
and let
t
t
approach
∞
∞
since
lim
x
→
∞
e
x
=
∞
lim
x
→
∞
e
x
=
∞
.
lim
t
→
∞
arctan
(
t
)
lim
t
→
∞
arctan
(
t
)
Step 3
The
limit
as
t
t
approaches
∞
∞
is
π
2
π
2
.
π
2
π
2
lim
x
→
∞
(
a
r
c
t
a
n
(
e
x
)
)
lim
x
→
∞
(
a
r
c
t
a
n
(
e
x
)
)
(
(
)
)
|
|
[
[
]
]
√
√
≥
≥
∫
∫
7
7
8
8
9
9
≤
≤
°
°
θ
θ
4
4
5
5
6
6
/
/
^
^
×
×
>
>
π
π
1
1
2
2
3
3
-
-
+
+
÷
÷
<
<
∞
∞
!
!
,
,
0
0
.
.
%
%
=
=
⎡
⎢
⎣
x
2
1
2
√
π
∫
x
d
x
⎤
⎥
⎦
[
x
2
1
2
π
∫
x
d
x
]
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