3 Group 8
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Question 1.
If
cos
α
=
-
3
2
,
α
∈
(
0
,
π
)
, then
a)
tg
α
=
-
1
b)
tg
α
=
-
3
3
c)
tg
α
is not defined
d)
tg
α
=
3
3
e)
tg
α
=
0
Question 2.
Determine
lim
n
→
∞
(
n
+
1
)
3
-
n
(
n
2
+
3
)
n
+
1000
.
a)
3
b)
1
c)
1
1000
d)
+
∞
e)
0
Question 3.
The maximal domain of definition of the function
f
(
x
)
=
log
(
|
x
|
-
3
)
is
a)
(
-
∞
,
-
4
⟩
∪
⟨
4
,
∞
)
b)
⟨
-
4
,
4
⟩
c)
ℝ
-
{
-
4
,
-
3
,
3
,
4
}
d)
(
-
3
,
3
)
e)
(
-
∞
,
-
3
)
∪
(
3
,
∞
)
Question 4.
Compute
lim
x
→
+
∞
tg
(
π
-
arctg
x
)
, if exists.
a)
1
b)
-
∞
c)
+
∞
d)
0
e)
does not exist
Evaluate