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Recent questions in Continuity and Differentiability
Questions
>>
CBSE XII
>>
Math
>>
Continuity and Differentiability
Find
d
y
d
x
when
y
=
tan
−
1
[
x
1
3
+
a
1
3
1
−
x
1
3
a
1
3
]
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q39
p14
easy
math
sec-a
asked
Jan 28, 2013
by
meena.p
1
answer
If
y
=
|
cos
x
|
+
|
sin
x
|
,
f
i
n
d
d
y
d
x
a
t
x
=
2
π
3
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q38
p14
medium
math
sec-b
asked
Jan 28, 2013
by
meena.p
1
answer
If
y
=
1
√
b
2
−
a
2
l
o
g
[
√
b
+
a
+
√
b
−
a
tan
x
2
√
b
+
a
−
√
b
−
a
tan
x
2
]
prove that
d
y
d
x
=
sec
2
x
2
(
b
+
a
)
−
(
b
−
a
)
tan
2
x
2
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q37
p14
difficult
math
sec-b
asked
Jan 28, 2013
by
meena.p
1
answer
A card from a pack of 52 playing cards is lost. Two cards are drawn from the remaining cards and found to be both spade. (i) Find the probability of lost card being a spade card.(ii)While playing in ground you found a purse containing rupees and some other documents,what will you do?
cbse
class12
modelpaper
2012
sec-c
q29
math
asked
Jan 25, 2013
by
thanvigandhi_1
1
answer
Write the number of one-one function from the set A = {1, 2, 3} to itself.
cbse
class12
modelpaper
2012
sec-a
q1
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
What is the value of
|
4
I
3
|
,
where
I
3
is the identity matrix of order 3?
cbse
class12
modelpaper
2012
sec-a
q3
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
If
√
1
−
x
2
+
√
1
−
y
2
=
a
(
x
−
y
)
,
p
r
o
v
e
t
h
a
t
d
y
d
x
=
√
1
−
y
2
1
−
x
2
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q36
p14
difficult
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Prove that
d
d
x
[
1
4
√
2
l
o
g
|
x
2
+
√
2
x
+
1
x
2
−
√
2
x
+
1
|
+
1
2
√
2
tan
−
1
√
2
x
1
−
x
2
]
=
1
1
+
x
4
cbse
class12
kvquestionbank2012
ch5
q34
p13
difficult
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Let
y
=
tan
−
1
[
4
x
1
+
5
x
2
]
+
tan
−
1
[
2
+
3
x
3
−
2
x
]
,
show that
d
y
d
y
=
5
1
+
25
x
2
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q33
p13
medium
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Given that
cos
x
2
.
cos
x
4
.
cos
x
8
.
.
.
.
.
.
.
=
sin
x
x
,
P
r
o
v
e
t
h
a
t
1
2
2
sec
2
x
2
+
1
2
4
sec
2
x
4
+
.
.
.
.
.
.
.
=
c
o
s
e
c
2
x
−
1
x
2
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q31
p13
difficult
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Find
d
y
d
x
,
when
y
=
sin
−
1
[
x
√
1
−
x
−
√
x
√
1
−
x
2
]
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q30
p13
medium
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Differentiate w.r.t. x,
y
=
tan
−
1
[
a
cos
x
−
b
sin
x
b
cos
x
+
a
sin
x
]
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q29
p13
medium
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
If
y
=
2
√
a
2
−
b
2
tan
−
1
[
√
a
−
b
a
+
b
tan
x
2
]
,
prove that
d
y
d
x
=
1
a
+
b
cos
x
,
a
>
b
>
0
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q28
p13
difficult
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
If
y
=
sin
−
1
[
x
2
√
1
−
x
2
+
x
√
1
−
x
4
]
,
prove that
d
y
d
x
=
2
x
√
1
−
x
4
+
1
√
1
−
x
2
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q27
p13
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Find
d
y
d
x
w
h
e
n
y
=
sin
−
1
[
5
x
+
12
√
1
−
x
2
13
]
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q26
p13
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Let
ϕ
(
x
)
a
n
d
h
(
x
)
be derivable at x = c. Show that necessary and sufficient condition for the function defined as :
f
(
x
)
=
{
ϕ
(
x
)
,
x
≤
c
h
(
x
)
,
x
>
c
to be derivable at x= c are
(
i
)
ϕ
(
c
)
=
h
(
c
)
(
i
i
)
ϕ
′
(
c
)
=
h
′
(
c
)
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q25
p13
medium
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Let
f
(
x
)
=
{
1
−
s
i
n
3
x
3
c
o
s
2
x
,
i
f
x
<
π
2
a
,
i
f
x
=
π
2
b
(
1
−
s
i
n
x
)
(
π
−
2
x
)
2
,
i
f
x
>
π
2
.
If f(x) is continuous function at x
x
=
π
2
, find a and b.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q24
p13
medium
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Discuss the continuity of the following function at x = 0
f
(
x
)
=
{
x
4
+
x
3
+
2
x
2
tan
−
1
x
,
x
≠
0
10
,
x
=
0
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q23
p12
medium
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Let
f
(
x
)
=
{
|
x
|
cos
1
x
i
f
x
≠
0
0
i
f
x
=
0
then discuss the continuity of f(x) at x = 0
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q22
p12
medium
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Find all the points of discontinuity of f defined by f(x) = | x | - | x+1|.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q21
p12
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
The function
l
o
g
(
1
+
a
x
)
−
l
o
g
(
1
−
b
x
)
x
is not defined at x = 0. Find the value of f(x) so that f(x) is continuous at x = 0.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q20
p12
medium
sec-a
math
asked
Jan 25, 2013
by
meena.p
1
answer
Show that the function
f
(
x
)
=
|
sin
x
+
cos
x
|
is continuous at
x
=
π
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q19
p12
medium
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Determine the values of a, b and c for which the function :
f
(
x
)
=
{
sin
(
a
+
1
)
x
+
sin
x
x
,
x
<
0
c
,
x
=
0
√
x
+
b
x
2
−
√
x
b
√
x
3
,
x
>
0
may continuous at x = 0
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q18
p12
medium
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Show that the function
f
(
x
)
=
{
x
+
λ
,
x
<
1
λ
x
2
+
1
,
x
≥
1
is continuous function, regardless of the choice of
λ
∈
R
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q17
p12
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Show that Sin | x | is continuous.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q16
p12
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Show that the function :
f
(
x
)
=
{
|
x
|
,
x
≤
2
[
x
]
,
x
>
2
is continuous [0,2].
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q15
p12
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Find a and b if the function :
f
(
x
)
=
{
[
1
+
|
sin
x
|
]
a
sin
|
x
|
,
−
π
6
<
x
<
0
6
,
x
=
0
e
tan
2
x
tan
3
x
,
0
<
x
<
π
6
is continuous on
(
−
π
6
,
π
6
)
.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q14
p12
math
sec-b
asked
Jan 25, 2013
by
meena.p
0
answers
Is the function
f
(
x
)
=
3
x
+
4
tan
x
x
continuous at x = 0? If not, how may the function be defined to make it continuous at this point.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q13
p11
easy
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Given that
f
(
x
)
=
{
1
−
cos
4
x
x
2
,
i
f
x
<
0
a
,
i
f
x
=
0
√
x
√
16
+
√
x
−
4
,
i
f
x
>
0
.
If f(x) is continuous at x = 0, find the value of a.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q11
p11
medium
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Find
d
y
d
x
when
y
=
tan
−
1
1
+
x
2
1
−
x
2
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q10
p11
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Find
d
y
d
x
when
y
=
a
x
.
x
a
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q9
p11
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Verify Rolles theorem for the function
f
(
x
)
=
sin
2
x
i
n
[
0
,
π
2
]
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q8
p11
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Let
y
=
y
=
√
e
√
x
,
x
>
0
f
i
n
d
d
y
d
x
.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q7
p11
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
If
f
(
x
)
=
|
x
x
2
x
3
1
2
x
3
x
2
0
2
6
x
|
than find
f
′
(
x
)
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q6
p11
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
If
f
1
(
x
)
=
g
(
x
)
a
n
d
g
1
(
x
)
=
−
f
(
x
)
for all n and
f
(
2
)
=
f
1
(
2
)
=
4
,
find the value of
f
2
(
24
)
+
g
2
(
24
)
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q5
p11
math
sec-a
asked
Jan 24, 2013
by
meena.p
1
answer
Find the set of all points where the function f(x) = 2x |x| is differentiable.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q4
p11
easy
math
sec-a
asked
Jan 24, 2013
by
meena.p
1
answer
Find
d
y
d
x
w
h
e
n
y
=
x
x
x
x
.
.
.
.
.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q3
p11
easy
math
sec-a
asked
Jan 24, 2013
by
meena.p
1
answer
Let f be a non zero continuous function satisfying f(x+y) = f(x).f(y) for all x, y
ϵ
R. If f(2) = 9 then find the value of f(3).
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q2
p11
easy
math
sec-a
asked
Jan 24, 2013
by
meena.p
1
answer
Let f be continuous function on [1,3]. If f takes only rational values for all x and f(2) = 10 then find the value of f(1.5)
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q1
p11
easy
math
sec-a
asked
Jan 24, 2013
by
meena.p
1
answer
True or False: If f.g is continuous at
x
=
a
,then f and g are separately continuous at
x
=
a
.
cbse
class12
ch5
q106
p116
true-or-false
exemplar
sec-a
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
True or False: Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.
cbse
class12
ch5
q105
p116
true-or-false
exemplar
sec-a
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
True or False: The composition of two continuous functions is a continuous function.
cbse
class12
ch5
q104
p116
true-or-false
exemplar
sec-a
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
True or False: If f is continuous on its domain D ,then | f | is also continuous on D.
cbse
class12
ch5
q103
p116
true-or-false
exemplar
sec-a
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
True or False: Rolle's theorem is applicable for the function
f
(
x
)
=
|
x
−
1
|
in [0,2].
cbse
class12
ch5
q102
p116
true-or-false
exemplar
sec-a
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
If
y
=
y
(
x
)
satisfies
x
cos
y
+
y
cos
x
=
π
, then find
y
″
(
0
)
:
cbse
class12
ch5
math
differential-equations
additionalproblem
jeemain
difficult
sec-b
asked
Jan 3, 2013
by
sreemathi.v
1
answer
If
f
(
x
)
=∣
cos
x
−
sin
x
∣
,
t
h
e
n
f
′
(
π
3
)
=__________.
cbse
class12
ch5
q100
p116
fitb
exemplar
sec-a
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
If
f
(
x
)
=∣
cos
x
∣
,then
f
′
(
π
4
)
=____________.
cbse
class12
ch5
q99
p116
fitb
exemplar
sec-a
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
Derivative of
x
2
w.r.t
x
3
is _____________.
cbse
class12
ch5
q98
p116
fitb
exemplar
sec-b
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
An example of a function which is continuous everywhere but fails to be differentiable exactly at two point is ____________.
cbse
class12
ch5
q97
p116
fitb
exemplar
sec-b
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
For the function
f
(
x
)
=
x
+
1
x
,
x
∈
[
1
,
3
]
,the value of c for mean value theorem is
cbse
class12
ch5
q96
p116
objective
exemplar
sec-a
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
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