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Byju's Answer
Standard XII
Mathematics
Integral as Antiderivative
Thefunction ...
Question
Thefunction
f
(
x
)
=
x
2
sin
1
x
,
x
≠
0
,
f
(
0
)
=
0
at
x
=
0
A
Is continuous but not differentiable
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B
Is having continuous derivative
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C
Is continuous
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D
Is continuous and differentiable
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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.
If
f
x
=
1
1
+
e
1
/
x
,
x
≠
0
0
,
x
=
0
then f (x) is
(a) continuous as well as differentiable at x = 0
(b) continuous but not differentiable at x = 0
(c) differentiable but not continuous at x = 0
(d) none of these
Q.
Show that the function
f
x
=
x
m
sin
1
x
,
x
≠
0
0
,
x
=
0
(i) differentiable at x = 0, if m > 1
(ii) continuous but not differentiable at x = 0, if 0 < m < 1
(iii) neither continuous nor differentiable, if m ≤ 0
Q.
The function f (x) = e
−
|x|
is
(a) continuous everywhere but not differentiable at x = 0
(b) continuous and differentiable everywhere
(c) not continuous at x = 0
(d) none of these
Q.
The function f(x) = e
|x|
is
(a) continuous every where but not differentiable at x = 0
(b) continuous and differentiable everywhere
(c) not continuous at x = 0
(d) none of these
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