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Byju's Answer
Standard XII
Mathematics
L'Hospital Rule to Remove Indeterminate Form
Let f:R→ R ...
Question
Let
f
:
R
→
R
be a differentiable function and
f
(
1
)
=
4.
Then the value of
lim
x
→
1
∫
f
(
x
)
4
2
t
x
−
1
d
t
is
A
8
f
′
(
1
)
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B
4
f
′
(
1
)
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C
2
f
′
(
1
)
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D
f
′
(
1
)
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Solution
The correct option is
A
8
f
′
(
1
)
lim
x
→
1
∫
f
(
x
)
4
2
t
x
−
1
d
t
=
lim
x
→
1
∫
f
(
x
)
4
2
t
d
t
x
−
1
Applying L'Hospital's rule
=
lim
x
→
1
2
f
(
x
)
f
′
(
x
)
1
=
f
(
1
)
f
′
(
1
)
=
8
f
′
(
1
)
Suggest Corrections
0
Similar questions
Q.
Let f:R
→
R is differentiable function &
f
(
1
)
=
4
, then
g
(
x
)
=
lim
x
→
1
∫
f
(
x
)
4
2
t
x
−
1
d
t
equals
Q.
Let
f
(
x
)
be a differentiable function and
f
(
1
)
=
2
.
If
lim
x
→
1
∫
f
(
x
)
2
2
t
x
−
1
d
t
=
4
, then the value of
f
′
(
1
)
, is
Q.
Let
f
:
R
→
R
be a differentiable function at
x
=
1
such that
f
(
1
)
=
4
and
f
′
(
1
)
=
2
and
α
=
lim
x
→
1
∫
f
(
x
)
4
2
t
x
−
1
d
t
, then
α
is
Q.
Let
f
:
R
→
R
be such that f(1) =2, f'(1)= 4 then the
lim
x
→
0
[
f
(
1
+
x
+
x
2
)
+
x
f
(
1
+
x
)
f
(
1
)
]
1
x
(
x
+
1
)
= _______
Q.
Let
F
:
R
→
R
be a differentiable function such that
F
(
x
)
=
∫
f
(
x
)
4
16
t
3
x
−
3
d
t
,
f
(
3
)
=
4
&
f
′
(
3
)
=
1
16
then the value of
lim
x
→
3
F
(
x
)
is
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