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KVPY SX SB Exam 2015 Question Paper
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© examsnet.com
Question : 10
Total: 120
The value of the limit
lim
x
→
0
(
x
sin
x
)
6
∕
x
2
is -
e
e
–
1
e
−
1
∕
6
e
6
Validate
Solution:
lim
x
→
0
(
x
sin
x
)
6
∕
x
2
(
1
)
∞
lim
e
x
→
0
6
x
2
(
x
sin
−
1
)
lim
e
x
→
0
6
x
2
(
x
−
sinx
sinx
)
lim
e
x
→
0
6
x
2
{
x
−
(
x
−
x
3
3
!
+
x
5
5
!
.
.
.
)
(
x
−
x
3
3
!
+
x
5
5
!
.
.
.
)
}
lim
e
x
→
0
6
x
2
{
x
3
3
!
+
x
5
5
!
.
.
.
}
(
x
−
x
3
3
!
+
x
5
5
!
.
.
.
)
lim
e
x
→
0
6
x
3
x
2
{
1
3
!
+
x
2
5
!
.
.
.
}
{
1
−
x
2
3
!
.
.
.
}
=
e
1
© examsnet.com
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