Question

Fin limx→0(cotx)(1−cos2x)x=2?

Answer 1

Answer:
lim
x
→
0

(
cot
x
)
(
1
−
cos
2
x
)
x
=
2
Explanation:
We seek:
L
=
lim
x
→
0

(
cot
x
)
(
1
−
cos
2
x
)
x



=
lim
x
→
0

(
cos
x
sin
x
)
(
1
−
(
cos
2
x
−
sin
2
x
)
)
x



=
lim
x
→
0

(
cos
x
sin
x
)
(
1
−
(
1
−
sin
2
x
−
sin
2
x
)
)
x



=
lim
x
→
0

(
cos
x
sin
x
)
(
2
sin
2
x
)
x



=
lim
x
→
0

(
cos
x
)
2
sin
x
x



=
2
lim
x
→
0

(
cos
x
)
(
sin
x
x
)



=
2
{
lim
x
→
0

(
cos
x
)
}
{
lim
x
→
0

(
sin
x
x
)
}



=
2
⋅
1
⋅
1



=
2