3 Group 14
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Question 1.
If
sin
(
α
+
π
)
=
-
1
, then
a)
cotg
α
=
0
b)
cotg
α
=
3
3
c)
cotg
α
=
3
d)
cotg
α
=
1
e)
cotg
α
is not defined
Question 2.
Determine
lim
n
→
∞
n
2
(
n
+
1
)
-
1
1
+
3
n
-
1000
n
2
.
a)
1
1000
b)
-
1
c)
0
d)
-
∞
e)
-
1
1000
Question 3.
The maximal domain of definition of the function
f
(
x
)
=
log
(
1
-
sin
x
)
is
a)
ℝ
-
⋃
k
∈
ℤ
{
k
π
2
}
b)
ℝ
-
⋃
k
∈
ℤ
{
3
2
π
+
2
k
π
}
c)
ℝ
-
⋃
k
∈
ℤ
{
1
2
π
+
2
k
π
}
d)
⋃
k
∈
ℤ
(
k
π
,
(
k
+
1
)
π
)
e)
ℝ
Question 4.
Compute
lim
x
→
+
∞
tg
(
π
-
arctg
x
)
, if exists.
a)
does not exist
b)
1
c)
0
d)
-
∞
e)
+
∞
Evaluate