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Standard XII
Mathematics
Substitution Method to Remove Indeterminate Form
Question
lim
x
→
0
1
−
cos
3
x
x
sin
2
x
=
1
2
3
2
1
4
3
4
A
3
2
B
1
4
C
1
2
D
3
4
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Solution
Verified by Toppr
lim
x
→
0
1
−
cos
3
x
x
sin
2
x
=
lim
x
→
0
(
1
−
cos
x
)
(
1
+
cos
x
+
cos
2
x
)
x
sin
2
x
=
lim
x
→
0
2
sin
2
x
2
(
1
+
cos
x
+
cos
2
x
)
4
x
cos
x
sin
x
2
cos
x
2
=
lim
x
→
0
sin
x
2
(
1
+
cos
x
+
cos
2
x
)
4
×
x
2
cos
x
2
×
cos
x
=
3
4
...... As
{
lim
x
2
→
0
sin
x
2
x
2
=
0
}
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