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Byju's Answer
Standard XII
Mathematics
Chain Rule of Differentiation
If fx is diff...
Question
If f (x) is differentiable at x = c, then write the value of
lim
x
→
c
f
x
.
Open in App
Solution
Given:
f
(
x
)
is differentiable at
x
=
c
. Then,
lim
x
→
c
f
(
x
)
-
f
(
c
)
x
-
c
exists finitely.
or,
lim
x
→
c
f
(
x
)
-
f
(
c
)
x
-
c
=
f
'
(
c
)
.
Consider,
lim
x
→
c
f
(
x
)
=
lim
x
→
c
f
(
x
)
-
f
(
c
)
x
-
c
(
x
-
c
)
+
f
(
c
)
lim
x
→
c
f
(
x
)
=
lim
x
→
c
f
(
x
)
-
f
(
c
)
x
-
c
(
x
-
c
)
+
f
(
c
)
lim
x
→
c
f
(
x
)
=
lim
x
→
c
f
(
x
)
-
f
(
c
)
x
-
c
lim
x
→
c
(
x
-
c
)
+
f
(
c
)
lim
x
→
c
f
(
x
)
=
f
'
(
c
)
×
0
+
f
(
c
)
=
f
(
c
)
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0
Similar questions
Q.
Let
f
(
x
)
be a function differentiable at
x
=
c
. Then
lim
x
→
c
f
(
x
)
equals
Q.
Let
f
:
R
→
R
be differentiable at
x
=
0
. If
f
(
0
)
and
f
′
(
0
)
=
2
, then the value of
lim
x
→
0
1
x
[
f
(
x
)
+
f
(
2
x
)
+
f
(
3
x
)
+
.
.
.
+
f
(
2015
x
)
]
is
Q.
Let f be a function satisfying the condition
λ
f
(
x
y
)
=
f
(
x
)
y
+
f
(
y
)
x
∀
x, y
>
0
. If
f
(
x
)
is differentiable and
f
(
1
)
=
1
, then the value of
lim
x
→
∞
x
f
(
x
)
is?
Q.
Write the value of
l
i
m
x
→
0
f
(
x
)
−
f
(
x
)
x
−
c
Q.
Assertion :The function
f
(
x
)
=
⎧
⎨
⎩
|
x
|
+
3
∀
x
≤
−
3
−
2
x
∀
−
3
<
x
<
3
6
x
+
2
∀
x
≥
3
is continuous for
−
3
≤
x
<
3
&
x
>
3
& non differentiable at
x
=
3
. Reason: If
lim
x
→
a
f
(
x
)
=
f
(
a
)
then
f
(
x
)
is continuous and if L.H.D at
x
=
a
=R.H.D at
x
=
a
then
f
(
x
)
is non differentiable at
x
=
0
.
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