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Recent questions in Limit, Continuity and Differentiability
Questions
>>
JEEMAIN and NEET
>>
Mathematics
>>
Limit, Continuity and Differentiability
lim
x
→
2
t
a
n
(
x
−
2
)
|
x
2
+
(
k
−
2
)
x
−
x
k
|
(
x
−
2
)
2
=
5
..find k
asked
Mar 30, 2015
by
sachinmalhotra.jan11
1
answer
find dy/dx . if y = (x/a+)(x/b+)(x/a+)(x/b+)(...................
asked
Nov 8, 2014
by
vishavjeetmor
1
answer
If
f
(
x
)
=
{
x
3
+
x
2
−
16
x
+
20
(
x
−
2
)
2
w
h
e
n
x
≠
3
k
w
h
e
n
x
=
2
and
f
(
x
)
is continuous at
x
=
3
find the value of k.
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
asked
Apr 22, 2014
by
meena.p
1
answer
If
f
(
x
)
=
{
|
x
+
2
|
tan
−
1
(
x
+
2
)
x
≠
−
2
2
x
=
−
2
then
f
(
x
)
is
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
asked
Apr 22, 2014
by
meena.p
1
answer
If the function
f
(
x
)
=
{
3
a
x
+
b
f
o
r
x
>
1
11
f
o
r
x
=
1
5
a
x
−
2
b
f
o
r
x
<
1
is continuous at
x
=
1
.find the values of a and b .
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
asked
Apr 22, 2014
by
meena.p
1
answer
If
f
(
x
+
y
)
=
f
(
x
)
.
f
(
y
)
for all x and y and if
f
(
5
)
=
2
and
f
′
(
0
)
=
3
find
f
′
(
5
)
jeemain
math
ch13
limits and derivatives
derivatives
difficult
asked
Apr 22, 2014
by
meena.p
1
answer
Find the values of K. So that the function
f
(
x
)
=
{
k
cos
x
π
−
2
x
i
f
x
≠
π
2
3
i
f
x
=
π
2
is continuous at
x
=
π
2
.
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
asked
Apr 22, 2014
by
meena.p
1
answer
Determine the value of K so that the function.
f
(
x
)
=
{
K
x
2
i
f
x
≤
2
3
i
f
x
>
2
is continuous .
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
asked
Apr 22, 2014
by
meena.p
1
answer
Evaluate
lim
x
→
π
/
6
(
√
3
sin
x
−
cos
x
)
(
x
−
π
/
6
)
jeemain
math
ch13
limits and derivatives
limits-of-trigonometric-functions
medium
asked
Apr 22, 2014
by
meena.p
1
answer
Evaluate
lim
x
→
0
(
x
3
cot
x
1
−
cos
x
)
jeemain
math
ch13
limits and derivatives
limits of trigonometrix functions
medium
asked
Apr 22, 2014
by
meena.p
1
answer
Evaluate
lim
x
→
0
(
sin
2
x
+
sin
6
x
sin
5
x
−
sin
3
x
)
jeemain
math
ch13
limits and derivatives
limits of trigonometric funtions
easy
asked
Apr 22, 2014
by
meena.p
1
answer
Evaluate
lim
x
→
2
(
e
x
−
e
2
x
−
2
)
jeemain
math
ch13
limits and derivatives
introduction to limits
medium
asked
Apr 22, 2014
by
meena.p
1
answer
Define
f
(
0
)
so that
f
(
x
)
=
(
x
+
1
)
cot
x
becomes continuous at
x
=
0
jeemain
math
ch13
limits and derivatives
introduction to limits
easy
asked
Apr 22, 2014
by
meena.p
1
answer
The function
f
(
x
)
=
|
x
|
x
2
+
2
x
x
≠
0
and
f
(
0
)
=
0
is not continuous at
x
=
0
because
cl23078
jeemain
math
ch13
limits and derivatives
introduction to limits
difficult
q187
asked
Mar 26, 2014
by
balaji
1
answer
The range of the function
f
(
x
)
=
x
2
+
x
+
2
x
2
+
x
+
1
,
x
∈
(
−
∞
,
∞
)
is:
jeemain
math
ch2
relations and functions
functions
difficult
q187
asked
Jan 6, 2014
by
sreemathi.v
1
answer
If the function
f
(
x
)
=
{
(
cos
x
)
1
/
x
x
≠
0
k
x
=
0
is continuous at
x
=
0
then value of
K
is
jeemain
math
ch13
limits and derivatives
limits-of-trigonometric-functions
difficult
q186
asked
Jan 6, 2014
by
sreemathi.v
1
answer
The value of
f
(
0
)
so that
f
(
x
)
=
(
4
x
−
1
)
3
sin
(
x
4
)
log
(
1
+
x
2
3
)
is continuous everywhere is
jeemain
math
ch13
limits and derivatives
introduction to trigonometric functions
difficult
q185
mock
asked
Jan 6, 2014
by
sreemathi.v
1
answer
let
α
and
β
be the distinct roots of
a
x
2
+
b
x
+
c
=
0
then
lim
x
→
α
1
−
cos
(
a
x
2
+
b
x
+
c
)
(
x
−
α
)
2
is equal to
jeemain
math
ch13
limits and derivatives
limits-of-trigonometric-functions
difficult
q184
asked
Jan 6, 2014
by
sreemathi.v
1
answer
lim
x
→
1
sin
(
e
x
−
1
)
log
x
is
jeemain
math
ch13
limits and derivatives
limits-of-trigonometric-functions
difficult
q183
asked
Jan 6, 2014
by
sreemathi.v
1
answer
lim
x
→
∞
cos
(
x
2
)
cos
(
x
4
)
cos
(
x
8
)
.
.
.
.
.
.
.
.
cos
(
x
2
n
)
is
jeemain
math
ch13
limits and derivatives
limits-of-trigonometric-functions
difficult
q182
asked
Jan 6, 2014
by
sreemathi.v
1
answer
If
α
,
β
are roots of
a
x
2
+
b
x
+
c
=
0
then
lim
x
→
α
1
−
cos
(
a
x
2
+
b
x
+
c
)
(
x
−
α
)
2
is
jeemain
math
ch13
limits and differentiability
introduction to limits
difficult
q181
asked
Jan 6, 2014
by
sreemathi.v
1
answer
lim
x
→
a
(
[
(
a
1
/
2
+
x
1
/
2
a
1
/
4
−
x
1
/
4
)
−
1
−
2
(
a
x
)
1
/
4
x
3
/
4
−
a
1
/
4
x
1
/
2
+
a
1
/
2
x
1
/
4
−
a
3
/
4
]
−
1
−
(
√
2
)
log
4
a
)
8
is
jeemain
math
ch13
limits and differentiability
introduction to limits
difficult
q180
asked
Jan 6, 2014
by
sreemathi.v
1
answer
The set of points where the function
f
(
x
)
=
√
1
−
e
−
x
2
is differentiable is
jeemain
math
ch5
continuity-and-differentiability
differentiability
difficult
q179
asked
Jan 6, 2014
by
sreemathi.v
1
answer
At the point
x
=
1
the function
f
(
x
)
=
{
x
3
−
1
1
<
x
<
∞
x
−
1
−
∞
<
x
≤
1
is
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q178
asked
Jan 6, 2014
by
sreemathi.v
1
answer
f
(
x
)
=
{
1
−
cos
4
x
x
2
x
<
0
a
x
=
0
√
x
√
[
16
+
√
x
]
−
4
x
>
0
If the function be continuous at
x
=
0
then
a
=
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q177
asked
Jan 6, 2014
by
sreemathi.v
1
answer
The function
f
(
x
)
=
{
x
+
a
√
2
sin
x
0
≤
x
<
π
4
2
x
cot
x
+
b
π
4
≤
x
<
π
2
a
cos
2
x
−
b
sin
x
π
2
<
x
≤
π
is continuous for
0
≤
x
≤
π
then a,b are
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q176
asked
Jan 6, 2014
by
sreemathi.v
1
answer
lim
x
→
0
x
(
1
+
a
cos
x
)
−
b
sin
x
x
3
=
1
then
a
,
b
are
jeemain
math
ch13
limits and derivatives
introduction to limits
difficult
q175
asked
Jan 6, 2014
by
sreemathi.v
1
answer
If
lim
x
→
∞
(
1
+
a
x
+
b
x
2
)
2
x
=
e
2
then the value of a and b are
jeemain
math
ch13
limits and derivatives
introduction to limits
difficult
q174
asked
Jan 6, 2014
by
sreemathi.v
1
answer
Let
f
(
a
)
=
g
(
a
)
=
k
and their
n
t
h
derivatives
f
(
n
)
(
a
)
,
g
(
n
)
(
a
)
exist and are not equal for some n. Further if
lim
x
→
a
f
(
a
)
g
(
x
)
−
f
(
a
)
−
g
(
a
)
f
(
x
)
+
g
(
a
)
g
(
x
)
−
f
(
x
)
=
4
then the value of K is
jeemain
math
ch13
limits and derivatives
derivatives
difficult
q173
asked
Jan 6, 2014
by
sreemathi.v
1
answer
If
f
(
x
)
=
cot
−
1
[
3
x
−
x
3
1
−
3
x
2
]
and
g
(
x
)
=
cos
−
1
[
1
−
x
2
1
+
x
2
]
then
lim
x
→
a
f
(
x
)
−
f
(
a
)
g
(
x
)
−
g
(
a
)
0
<
a
<
1
2
is
jeemain
math
ch13
limits and derivatives
derivatives
difficult
q172
asked
Jan 6, 2014
by
sreemathi.v
1
answer
If
lim
x
→
a
a
x
−
x
a
x
x
−
a
a
=
−
1
and
a
>
0
then
a
=?
jeemain
math
ch13
limits and derivatives
introduction to limits
difficult
q171
asked
Jan 6, 2014
by
sreemathi.v
1
answer
Let
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
∀
x
,
y
∈
R
. Suppose that
f
(
3
)
=
3
and
f
′
(
0
)
=
11
, then
f
′
(
3
)
is given by
jeemain
math
ch13
limits and derivatives
derivatives
difficult
q170
asked
Jan 6, 2014
by
sreemathi.v
1
answer
If
α
is a repeated root of
a
x
2
+
b
x
+
c
=
0
, then
lim
x
→
α
sin
(
a
x
2
+
b
x
+
c
)
(
x
−
α
)
2
=
jeemain
math
ch13
limits and derivatives
introduction to limits
difficult
q169
asked
Jan 6, 2014
by
sreemathi.v
1
answer
lim
x
→
0
[
1
x
+
2
x
+
3
x
+
.
.
.
.
.
.
.
.
.
n
x
n
]
1
x
is
jeemain
math
ch13
limits and derivatives
introduction to limits
difficult
q168
asked
Jan 6, 2014
by
sreemathi.v
1
answer
The function
f
(
x
)
=
{
x
2
a
0
≤
x
<
1
a
1
≤
x
<
√
2
2
b
2
−
4
b
x
2
√
2
≤
x
<
∞
is continuous for
0
≤
x
<
∞
then the most suitable values of a and b are
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q167
asked
Jan 4, 2014
by
sreemathi.v
1
answer
Evaluate
lim
x
→
a
√
a
+
2
x
−
√
3
x
√
3
a
+
x
−
2
√
x
, where
a
≠
0
jeemain
math
ch13
limits and derivatives
introduction to limits
difficult
q166
asked
Jan 4, 2014
by
sreemathi.v
1
answer
The value of
lim
x
→
0
√
1
2
(
1
−
cos
2
x
)
x
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q165
asked
Jan 4, 2014
by
sreemathi.v
1
answer
If
f
(
x
)
=
x
2
−
1
, then on the interval
[
0
,
π
]
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q164
asked
Jan 4, 2014
by
sreemathi.v
1
answer
The set of all points where the function
f
(
x
)
=
x
(
1
+
|
x
|
)
is differentiable is
jeemain
math
ch5
continuity-and-differentiability
differentiability
difficult
q163
asked
Jan 4, 2014
by
sreemathi.v
1
answer
Let
[
x
]
denote the greatest integer less than or equal to x. If
f
(
x
)
=
[
x
sin
π
x
]
, then
f
(
x
)
is
jeemain
math
ch5
continuity-and-differentiability
differentiability
difficult
q162
asked
Jan 3, 2014
by
sreemathi.v
1
answer
If
f
(
x
)
=
x
(
√
x
−
√
x
+
1
)
then
jeemain
math
ch5
continuity-and-differentiability
differentiability
difficult
q161
asked
Jan 3, 2014
by
sreemathi.v
1
answer
If
x
+
|
y
|
=
2
y
, then
y
as a function of x is
jeemain
math
ch5
continuity-and-differentiability
differentiability
difficult
q160
asked
Jan 3, 2014
by
sreemathi.v
1
answer
Consider the function
f
(
x
)
=
|
x
−
2
|
+
|
x
−
5
|
x
∈
R
.
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q159
asked
Jan 3, 2014
by
sreemathi.v
1
answer
If
f
:
R
→
R
is a function defined by
f
(
x
)
=
[
x
]
cos
(
2
x
−
1
2
)
π
where [x] denotes the greatest integer function then f is
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q158
asked
Jan 3, 2014
by
sreemathi.v
1
answer
Let
f
(
x
)
=
[
x
]
sin
[
π
[
x
+
1
]
]
where [.] denotes the greatest integer function. The domain of
f
is and the point of discontinuity of
f
in the domain are
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q157
asked
Jan 3, 2014
by
sreemathi.v
1
answer
A
B
C
is an isosceles triangle inscribed in a circle of radius r. If
A
B
=
A
C
and
h
is the altitude from
A
to
B
C
, then the triangle
A
B
C
has perimeter
P
=
2
(
√
2
h
r
−
h
2
)
+
√
2
h
r
)
and area
A
=_______also
lim
h
→
0
A
p
3
=
_______
jeemain
math
ch13
limits and derivatives
introduction to limits
difficult
q156
asked
Jan 3, 2014
by
sreemathi.v
1
answer
lim
x
→
0
x
tan
2
x
−
2
x
tan
x
(
1
−
cos
2
x
)
2
is
jeemain
math
ch13
limits and derivatives
limits of triginometric functions
difficult
q155
asked
Jan 3, 2014
by
sreemathi.v
1
answer
The function
f
(
x
)
=
(
x
2
−
1
)
|
x
2
−
3
x
+
2
|
+
cos
(
|
x
|
)
is not differentiable at
jeemain
math
ch5
continuity-and-differentiability
differentiability
difficult
q154
asked
Jan 3, 2014
by
sreemathi.v
1
answer
The function
f
(
x
)
=
[
x
]
2
−
[
x
2
]
where
[
x
]
is the greatest integer less than or equal to x, is discontinuous at
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q153
asked
Jan 3, 2014
by
sreemathi.v
1
answer
The function
f
:
R
{
0
}
→
R
given by
f
(
x
)
=
1
x
−
2
e
2
x
−
1
can be made continuous at
x
=
0
by defining f(0) as
jeemain
math
ch5
continuity-and-differentiability
continuity
difficult
q152
asked
Jan 3, 2014
by
sreemathi.v
1
answer
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