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Standard XII
Mathematics
Question
lim
x
→
0
e
x
−
e
sin
x
2
(
x
−
sin
x
)
=
1
3
2
−
1
2
1
2
A
1
B
1
2
C
3
2
D
−
1
2
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Solution
Verified by Toppr
We simplify the given expression as,
lim
x
→
0
e
s
i
n
x
(
e
x
−
s
i
n
x
−
1
)
2
(
x
−
s
i
n
x
)
Let
x
−
s
i
n
x
=
y
As
x
→
0
so does y
→
0
Hence, the question transforms into
(
lim
x
→
0
e
s
i
n
x
2
)
×
(
lim
y
→
0
e
y
−
1
y
)
=
1
2
×
1
=
1
2
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