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Recent questions and answers in Continuity and Differentiability
Questions
>>
CBSE XII
>>
Math
>>
Continuity and Differentiability
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
answered
Jun 24, 2019
by
premkht
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
answered
Feb 16, 2017
by
meena.p
1
answer
If
x
=
a
(
θ
−
sin
θ
)
;
y
=
a
(
1
+
cos
θ
)
find
d
2
y
d
x
2
at
θ
=
π
2
cbse
class12
ch5
additionalproblem
sec-b
q7
answered
Feb 16, 2017
by
meena.p
1
answer
Differentiate w.r.t.
x
the function in
x
x
+
x
a
+
a
x
+
a
a
, for some fixed
a
>
0
and
x
>
0
cbse
class12
maths
ch5
sec-e
answered
Dec 8, 2016
by
priyanka.c
1
answer
Find the slope of the tangent to the curve
x
2
+
y
2
=
4
x
−
2
at the point (3,1)
cbse
class12
ch5
additionalproblem
q13
answered
Apr 3, 2016
by
sarveshchauhan185
1
answer
Find points on the curve
y
=
x
2
+
1
at which the slope of the tangent is equal to its
x
coordinate.
cbse
class12
ch5
additionalproblem
q16
asked
May 1, 2014
by
meena.p
0
answers
Find the equation of normal to the curve
x
2
+
2
y
=
8
x
−
2
at the point
(
6
,
5
)
cbse
class12
ch5
additionalproblem
q15
asked
May 1, 2014
by
meena.p
0
answers
Find the equation of the tangent to the curve
√
x
+
√
y
=
a
at the point
(
a
2
4
,
a
2
4
)
cbse
class12
ch5
additionalproblem
q14
asked
May 1, 2014
by
meena.p
0
answers
Verify Mean value theorem for the following functions:
(
a
)
f
(
x
)
=
x
(
x
+
4
)
2
o
n
[
0
,
4
]
(
b
)
f
(
x
)
=
2
sin
x
+
sin
2
x
o
n
[
0
,
π
]
(
c
)
f
(
x
)
=
x
3
−
2
x
2
−
x
+
3
i
n
[
0
,
1
]
(
d
)
f
(
x
)
=
x
+
1
x
o
n
[
1
,
3
]
cbse
class12
ch5
additionalproblem
q12
asked
May 1, 2014
by
meena.p
0
answers
Verify Rolles theorem for the following functions:
(
a
)
f
(
x
)
=
x
2
−
5
x
+
4
o
n
[
0
,
4
]
(
b
)
f
(
x
)
=
x
(
x
−
1
)
2
o
n
[
0
,
1
]
(
c
)
f
(
x
)
=
x
3
−
7
x
2
+
16
x
−
12
o
n
[
2
,
3
]
(
d
)
f
(
x
)
=
e
x
(
sin
x
−
cos
x
)
o
n
[
π
4
,
5
π
4
]
cbse
class12
ch5
additionalproblem
q11
asked
May 1, 2014
by
meena.p
0
answers
If
y
=
√
1
−
x
2
+
x
√
1
−
y
2
=
1
prove that
d
y
d
x
=
(
−
1
)
√
1
−
y
2
1
−
x
2
cbse
class12
ch5
additionalproblem
q10
asked
May 1, 2014
by
meena.p
0
answers
If
√
1
−
x
2
+
√
1
−
y
2
=
a
(
x
−
y
)
,
a being a constant prove that
d
y
d
x
=
√
1
−
y
2
√
1
−
x
2
cbse
class12
ch5
additionalproblem
q9
asked
May 1, 2014
by
meena.p
0
answers
If
sin
x
=
y
sin
(
x
+
b
)
show that
d
y
d
x
=
sin
b
sin
2
(
x
+
b
)
cbse
class12
ch5
additionalproblem
q8
asked
May 1, 2014
by
meena.p
0
answers
If
y
=
[
x
+
√
x
2
+
1
]
m
show that
(
x
2
+
1
)
y
2
+
x
y
1
−
m
2
y
=
0
cbse
class12
ch5
additionalproblem
q6
asked
May 1, 2014
by
meena.p
0
answers
If
x
m
y
n
=
(
x
+
y
)
m
+
n
show that
d
y
d
x
=
y
x
cbse
class12
ch5
additionalproblem
q5
asked
May 1, 2014
by
meena.p
0
answers
Differentiate the following function:
(
x
cos
x
)
x
+
(
x
sin
x
)
1
x
cbse
class12
ch5
additionalproblem
q4
q4-5
asked
May 1, 2014
by
meena.p
0
answers
Differentiate the following function:
x
sin
x
+
cos
x
cbse
class12
ch5
additionalproblem
q4
q4-4
asked
May 1, 2014
by
meena.p
0
answers
Differentiate the following function:
x
cos
−
1
x
cbse
class12
ch5
additionalproblem
q4
q4-3
asked
May 1, 2014
by
meena.p
0
answers
Differentiate the following function:
tan
−
1
(
cos
x
1
+
sin
x
)
cbse
class12
ch5
additionalproblem
q4
q4-2
asked
May 1, 2014
by
meena.p
0
answers
Differentiate the following function:
tan
−
1
(
√
1
+
x
2
+
x
)
cbse
class12
ch5
additionalproblem
q4
q4-1
asked
May 1, 2014
by
meena.p
0
answers
Show that
f
(
x
)
=
|
x
−
2
|
is continuous but not derivable at
x
=
2
cbse
class12
ch5
additionalproblem
q3
asked
May 1, 2014
by
meena.p
0
answers
The function
f
(
x
)
is defined as follows :
f
(
x
)
=
{
x
2
+
a
x
+
b
0
≤
x
<
2
3
x
+
2
,
2
≤
x
≤
4
2
a
x
+
5
b
4
<
x
≤
8
If
f
is continuous on
[
0
,
8
]
find the values of a and b
cbse
class12
ch5
additionalproblem
q2
asked
May 1, 2014
by
meena.p
0
answers
Let
f
(
x
)
=
{
1
−
cos
4
x
x
2
,
x
<
0
a
,
x
=
0
√
x
)
(
√
16
+
√
x
)
−
4
x
<
0
Find
a
if
f
is continuous at
x
=
0
cbse
class12
ch5
additionalproblem
q1
asked
May 1, 2014
by
meena.p
0
answers
If
y
=
500
e
7
x
+
600
e
−
7
x
, what is
d
2
y
d
x
2
cl281
cbse
class12
bookproblem
ch5
sec7
q15
p184
sec-a
easy
math
answered
Apr 10, 2014
by
balaji.thirumalai
1
answer
If
y
=
3
cos
(
log
x
)
+
4
sin
(
log
x
)
, show that
x
2
y
2
+
x
y
1
cl279
cbse
class12
bookproblem
ch5
sec7
q13
p184
sec-a
easy
math
asked
Apr 10, 2014
by
balaji.thirumalai
1
answer
If
y
=
5
cos
x
−
3
sin
x
, what is
d
2
y
d
x
2
cl277
cbse
class12
bookproblem
ch5
sec7
q11
p183
sec-a
easy
math
answered
Apr 10, 2014
by
balaji.thirumalai
1
answer
For the curve
√
x
+
√
y
=
1
,
d
y
d
x
at
(
1
4
,
1
4
)
is ____________.
cl2460
cbse
class12
ch5
q101
p116
fitb
exemplar
sec-a
easy
math
answered
Mar 26, 2014
by
balaji.thirumalai
1
answer
If
√
1
−
y
2
−
√
1
−
x
2
=
a
(
x
−
y
)
,
then find
d
y
d
x
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q45
p14
sec-b
difficult
math
jeemain
limits-continuity-and-differentiability
asked
Feb 5, 2014
by
rvidyagovindarajan_1
1
answer
If
e
x
+
y
=
x
y
,
what is
d
y
d
x
?
cbse
class12
additionalproblem
ch5
sec-a
medium
math
jeemain
limits-continuity-and-differentiability
differentiability
answered
Jan 29, 2014
by
balaji
1
answer
If
(
x
=
√
a
s
i
n
−
1
t
,
y
=
√
a
c
o
s
−
1
t
)
,
what is the value of
d
y
d
x
cbse
class12
additionalproblem
ch5
sec-b
medium
math
jeemain
limits-continuity-and-differentiability
differentiability
answered
Dec 22, 2013
by
balaji.thirumalai
1
answer
If
x
y
y
x
=
100
, evaluate
d
y
d
x
cbse
class12
math
additionalproblem
jeemain
limits-continuity-and-differentiability
ch5
sec-a
differentiability
medium
answered
Dec 22, 2013
by
balaji.thirumalai
1
answer
If
x
√
1
+
y
+
y
√
1
+
x
=
0
,
Evaluate
d
y
d
x
class12
cbse
additionalproblem
ch5
easy
sec-a
math
jeemain
limits-continuity-and-differentiability
answered
Dec 22, 2013
by
balaji.thirumalai
1
answer
Find
d
y
d
x
if
(
(
x
2
+
y
2
)
2
=
x
y
)
cbse
class12
modelpaper
2012
sec-b
q21
easy
math
answered
Sep 23, 2013
by
sreemathi.v
1
answer
Discuss the continuity of the following functions
(
c
)
f
(
x
)
=
sin
x
.
cos
x
cbse
class12
ch5
sec1
q21
q21-c
p160
sec-a
easy
math
answered
Sep 11, 2013
by
sreemathi.v
1
answer
Discuss the continuity of the following functions
(
b
)
f
(
x
)
=
sin
x
−
cos
x
cbse
class12
ch5
sec1
q21
q21-b
p160
sec-a
easy
math
answered
Sep 11, 2013
by
sreemathi.v
1
answer
Discuss the continuity of the following functions
(
a
)
f
(
x
)
=
sin
x
+
cos
x
cbse
class12
ch5
sec1
q21
q21-a
p160
sec-a
easy
math
answered
Sep 11, 2013
by
sreemathi.v
1
answer
For what value of
λ
is the function defined by
f
defined by
f
(
x
)
=
{
λ
(
x
2
−
2
x
)
,
if
x
≤
0
4
x
+
1
,
if
x
> 0
Continuous at
x
=
0
?
cbse
class12
bookproblem
ch5
sec1
q18
q18-1
p160
sec-a
easy
math
answered
Aug 19, 2013
by
sreemathi.v
1
answer
A car, traveling with a uniform acceleration, has a velocity of 18 km/hour at a certain time and 54 km/hour after covering a distance of 500m. How much further will it travel to attain a velocity of 72 km/hour?
answered
Aug 18, 2013
by
vijayalakshmi_ramakrishnans
1
answer
A body falls freely from the top of a tower; It covers of the whole distance in the last second. Find the height of the tower and the total by the
asked
Aug 17, 2013
by
anilglpl_1
0
answers
A car, traveling with a uniform acceleration, has a velocity of 18 km/hour at a certain time and 54 km/hour after covering a distance of 500m. How much further will it travel to attain a velocity of 72 km/hour?
asked
Aug 17, 2013
by
anilglpl_1
0
answers
Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example?
(
i
)
f
(
x
)
=
[
x
]
f
o
r
x
∈
[
5
,
9
]
cbse
class12
bookproblem
ch5
sec8
q2
p186
math
sec-a
answered
Aug 16, 2013
by
sreemathi.v
1
answer
Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example?
(
i
i
i
)
f
(
x
)
=
x
2
−
1
f
o
r
x
∈
[
1
,
2
]
cbse
class12
bookproblem
ch5
sec8
q2
q2-3
p186
math
answered
Aug 16, 2013
by
sreemathi.v
1
answer
Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example?
(
i
i
)
f
(
x
)
=
[
x
]
f
o
r
x
∈
[
−
2
,
2
]
cbse
class12
bookproblem
ch5
sec8
q2
q2-2
p186
math
answered
Aug 16, 2013
by
sreemathi.v
1
answer
Find the value of
k
in the following so that the function
f
is continuous at the indicated point
f
(
x
)
=
{
1
−
cos
k
x
x
sin
x
,
i
f
x
≠
0
1
2
,
i
f
x
=
0
a
t
x
=
0
cbse
class12
ch5
q14
p108
short-answer
exemplar
sec-b
medium
math
answered
Jul 5, 2013
by
sreemathi.v
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
answered
Jul 5, 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
answered
Jul 5, 2013
by
sreemathi.v
1
answer
Show that
f
(
x
)
=
|
x
−
5
|
is continuous but not differentiable at
x
=
5
cbse
class12
ch5
q23
p109
short-answer
exemplar
sec-a
easy
math
answered
Jul 5, 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
answered
Jul 5, 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
answered
Jul 5, 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
answered
Jul 5, 2013
by
sreemathi.v
1
answer
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