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Byju's Answer
Standard XII
Mathematics
Derivative of Standard Functions
The function ...
Question
The function
f
(
x
)
=
{
1
−
2
x
+
3
x
2
−
4
x
3
+
.
.
.
.
∞
,
x
≠
−
1
1
,
x
=
−
1
is
A
Continuous at
x
=
−
1
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B
Neither continuous nor differential at
x
=
−
1
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C
differential at
x
=
−
1
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D
not differential at
x
=
−
1
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Solution
The correct options are
B
not differential at
x
=
−
1
C
Neither continuous nor differential at
x
=
−
1
For
x
≠
−
1
, we have
f
(
x
)
=
1
−
2
x
+
3
x
2
−
4
x
3
+
.
.
.
∞
=
(
1
+
x
)
−
1
=
1
1
+
x
lim
h
→
0
f
(
−
1
−
h
)
=
lim
h
→
0
1
1
−
1
−
h
→
−
∞
So,
f
(
x
)
is not continuous at
x
=
−
1
Also,
lim
h
→
0
f
(
−
1
−
h
)
−
f
(
−
1
)
(
−
1
−
h
)
−
(
−
1
)
=
lim
h
→
0
−
1
h
−
1
−
h
=
lim
h
→
0
1
+
h
h
2
→
∞
So,
f
(
x
)
is not derivable at
x
=
−
1
Hence,
f
(
x
)
is neither continuous nor derivable at
x
=
−
1
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0
Similar questions
Q.
If
f
x
=
1
-
cos
x
x
sin
x
,
x
≠
0
1
2
,
x
=
0
then at x = 0, f (x) is
(a) continuous and differentiable
(b) differentiable but not continuous
(c) continuous but not differentiable
(d) neither continuous nor differentiable
Q.
The function
f
(
x
)
=
x
tan
−
1
1
x
for
x
≠
0
,
f
(
0
)
=
0
is :
Q.
Let
f
(
x
)
=
tan
(
π
[
x
−
π
]
)
1
+
[
x
]
2
, where
[
.
]
denotes the greatest integer function. Then
Q.
Show that the function
f
(
x
)
=
⎧
⎨
⎩
x
2
,
x
≤
1
1
x
,
x
>
1
is continuous at
x
=
1
but not differentiable.
Q.
Show that the function
f
x
=
2
x
-
3
x
,
x
≥
1
sin
π
x
2
,
x
<
1
is continuous but not differentiable at x = 1.
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