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Byju's Answer
Standard XII
Mathematics
Right Hand Derivative
Let F:R → R b...
Question
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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Solution
F
(
x
)
=
∫
f
(
x
)
4
16
t
3
x
−
3
d
t
lim
x
→
3
F
(
x
)
=
lim
x
→
3
f
(
x
)
∫
4
16
t
3
x
−
3
d
t
=
lim
x
→
3
16
(
f
(
x
)
)
3
f
′
(
x
)
1
(
0
0
,
L-Hospital
)
=
16
×
4
3
1
×
1
16
=
64
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0
Similar questions
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
Q.
Let
f
:
R
→
[
3
,
5
]
be a differentiable function such that
lim
x
→
∞
(
f
(
x
)
+
f
′
(
x
)
)
=
3
then
lim
x
→
∞
f
(
x
)
Q.
Let
f
:
R
→
R
be a differentiable function satisfying
f
′
(
3
)
+
f
′
(
2
)
=
0
. Then
lim
x
→
0
(
1
+
f
(
3
+
x
)
−
f
(
3
)
1
+
f
(
2
−
x
)
−
f
(
2
)
)
1
/
x
is equal to :
Q.
Let
f
(
x
)
=
1
√
18
−
x
2
, then the value of
lim
x
→
3
f
(
x
)
−
f
(
3
)
x
−
3
is
Q.
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
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