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Byju's Answer
Standard XII
Mathematics
Substitution Method to Remove Indeterminate Form
limx→ 0sinπco...
Question
lim
x
→
0
sin
(
π
cos
2
x
)
x
2
is equal to.
A
−
π
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B
π
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C
π
2
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D
1
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Solution
The correct option is
A
π
lim
x
→
0
sin
(
π
cos
2
x
)
x
2
(
0
0
f
o
r
m
)
=
lim
x
→
0
{
cos
(
π
cos
2
x
)
⋅
π
⋅
2
cos
x
(
−
sin
x
)
}
2
x
(using L'Hospital's rule)
=
lim
x
→
0
π
cos
(
π
cos
2
x
)
⋅
cos
x
⋅
(
−
sin
x
x
)
=
(
π
)
⋅
(
−
1
)
⋅
1
⋅
(
−
1
)
=
π
.
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0
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