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Byju's Answer
Standard XII
Mathematics
Theorems for Differentiability
limx→03x-1/√x...
Question
lim
x
→
0
3
x
−
1
√
x
+
1
−
1
is equal to
A
log
e
9
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B
log
e
3
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C
0
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D
1
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Solution
The correct option is
C
log
e
9
lim
x
→
0
3
x
−
1
√
x
+
1
−
1
=
lim
x
→
0
3
x
−
1
√
x
+
1
−
1
×
√
x
+
1
+
1
√
x
+
1
+
1
lim
x
→
0
3
x
−
1
x
lim
x
→
0
√
x
+
1
+
1
=
log
3
×
2
=
2
log
3
=
log
9
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0
Similar questions
Q.
lim
x
→
0
(
3
x
−
1
x
)
is equal to
Q.
A function
f
:
R
→
R
+
satisfies
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
∀
x
,
y
∈
R
.
If
f
(
0
)
=
1
and
f
′
(
0
)
=
2
, then the value of
log
e
3
∫
0
[
f
(
x
)
e
−
x
]
d
x
is
(where
[
⋅
]
is represents the greatest integer function)
Q.
Find
lim
x
→
0
(
3
x
−
1
√
1
+
x
−
1
)
Q.
lim
x
→
0
3
x
+
1
x
+
3
Q.
Find
lim
x
→
0
f
(
x
)
and
lim
x
→
1
f
(
x
)
,
where
f
(
x
)
=
{
2
x
+
3
,
x
≤
0
3
(
x
+
1
)
,
x
>
0
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