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Byju's Answer
Standard XII
Mathematics
Expansions to Remove Indeterminate Form
The value of ...
Question
The value of
lim
h
→
0
2
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
√
3
sin
(
π
6
+
h
)
−
cos
(
π
6
+
h
)
√
3
h
(
√
3
cos
h
−
sin
h
)
⎫
⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪
⎭
is :
A
3
4
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B
2
√
3
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C
4
3
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D
2
3
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Solution
The correct option is
C
4
3
lim
h
→
0
2
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
√
3
sin
(
π
6
+
h
)
−
cos
(
π
6
+
h
)
√
3
h
(
√
3
cos
h
−
sin
h
)
⎫
⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪
⎭
=
lim
h
→
0
4
2
√
3
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
cos
(
π
6
)
sin
(
π
6
+
h
)
−
cos
(
π
6
+
h
)
sin
(
π
6
)
h
[
cos
(
π
6
)
cos
h
−
sin
h
sin
(
π
6
)
]
⎫
⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪
⎭
=
lim
h
→
0
2
√
3
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
sin
(
π
6
+
h
−
π
6
)
h
(
cos
(
h
+
π
6
)
)
⎫
⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪
⎭
=
lim
h
→
0
2
√
3
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
sin
(
h
)
h
cos
(
h
+
π
6
)
⎫
⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪
⎭
=
2
√
3
×
2
√
3
=
4
3
Suggest Corrections
0
Similar questions
Q.
The value of
lim
h
→
0
2
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
√
3
sin
(
π
6
+
h
)
−
cos
(
π
6
+
h
)
√
3
h
(
√
3
cos
h
−
sin
h
)
⎫
⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪
⎭
is :
Q.
lim
h
→
0
2
(
√
3
sin
(
π
6
+
h
)
−
cos
(
π
6
+
h
)
)
√
3
h
(
√
3
cos
h
−
sin
h
)
is equal to
Q.
lim
h
→
0
2
⎡
⎣
√
3
sin
(
π
6
+
h
)
−
cos
(
π
6
+
h
)
√
3
h
(
√
3
cosh
−
sinh
)
⎤
⎦
=
Q.
The value of
lim
h
→
0
2
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
√
3
sin
(
π
6
+
h
)
−
cos
(
π
6
+
h
)
√
3
h
(
√
3
cos
h
−
sin
h
)
⎫
⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪
⎭
is :
Q.
lim
2
h
→
0
3
sin
π
/
6
+
h
-
cos
π
/
6
+
h
3
h
3
cos
h
-
sin
h
is equal to
(a)
2/3
(
b
)
4/3
(
c
)
-
2
3
(d)
−4/3
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