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class 11
| maths
| continuity and differentiability
Solutions for all the questions from class 11
of subject maths
of chapter continuity and differentiability
CLASS
class 10
class 11
class 12
class 6
class 7
class 8
class 9
SUBJECT
maths
CHAPTER
application of derivatives
application of integrals
binomial theorem
circle
circles
complex numbers
complex numbers and quadratic equations
continuity and differentiability
coordinate geometry
daily practice problems
View All ↓
Class 11
Maths
Calculus
Continuity And Differentiability
If
y
=
e
−
x
cos
x
a
n
d
y
n
+
k
n
y
=
0
,
w
h
e
r
e
y
n
=
d
x
n
d
n
y
a
n
d
k
n
are constants
∀
n
∈
N
,
then (a)
k
4
=
4
(b)
k
8
=
−
1
6
(c)
k
1
2
=
2
0
(d)
k
1
6
=
−
2
4
Class 11
Maths
Calculus
Continuity And Differentiability
Let
g
(
x
)
=
f
(
x
)
sin
x
,
w
h
e
r
e
f
(
x
)
is a twice differentiable function on
(
−
∞
,
∞
)
such that
f
(
−
π
)
=
1
.
The value of
∣
∣
∣
g
−
π
∣
∣
∣
equals __________
Class 11
Maths
Calculus
Continuity And Differentiability
If
y
=
2
x
2
+
2
1
x
x
2
+
1
+
(
lo
g
)
e
x
+
x
2
+
1
, prove that
2
y
=
x
y
p
r
i
m
e
+
(
lo
g
)
e
y
p
r
i
m
e
,
w
h
e
r
e
y
′
denotes the derivative w.r.t
x
˙
Class 11
Maths
Calculus
Continuity And Differentiability
If
y
=
x
(
l
o
g
x
)
log
(
l
o
g
x
˙
)
,
t
h
e
n
d
x
d
y
i
s
(a)
x
y
(
1
n
x
∞
x
−
1
)
+
2
1
n
x
1
n
(
1
n
x
)
)
(b)
x
y
(
lo
g
x
)
log
(
l
o
g
x
)
(
2
lo
g
(
lo
g
x
)
+
1
)
(c)
x
1
n
x
y
[
(
1
n
x
)
2
+
2
1
n
(
1
n
x
)
]
(d)
x
y
lo
g
x
lo
g
y
[
2
lo
g
(
lo
g
x
)
+
1
]
Class 11
Maths
Calculus
Continuity And Differentiability
A nonzero polynomial with real coefficient has the property that
f
(
x
)
=
f
p
r
i
m
e
(
x
)
f
˙
p
r
i
m
e
p
r
i
m
e
(
x
)
˙
If
a
is the leading coefficient of
f
(
x
)
,
then the value of
2
a
1
is____
Class 11
Maths
Calculus
Continuity And Differentiability
Let
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
2
x
y
−
1
for all real
x
a
n
d
y
and
f
(
x
)
be a differentiable function. If
f
p
r
i
m
e
(
0
)
=
cos
α
,
the prove that
f
(
x
)
>
0
∀
x
∈
R
˙
Class 11
Maths
Calculus
Continuity And Differentiability
(
lim
)
x
0
sin
(
x
c
)
x
a
sin
b
x
, where a , b , c in R ~{0},exists and has non-zero value. Then,
a
+
c
= (a) b (b)
−
1
0
(d) none of these
Class 11
Maths
Calculus
Continuity And Differentiability
If
f
(
x
)
=
{
sin
x
2
x
=
n
π
and
n
∈
I
2
x
=
n
π
and
g
(
x
)
=
⎩
⎪
⎨
⎪
⎧
x
2
+
1
4
5
x
=
0
x
=
0
x
=
2
then
x
→
0
lim
g
{
f
(
x
)
}
is
Class 11
Maths
Calculus
Continuity And Differentiability
If
x
=
t
2
,
y
=
t
3
,
t
h
e
n
d
x
2
d
2
y
=
(a)
2
3
(b)
(
4
t
)
3
(c)
2
(
t
)
3
(d)
2
3
t
Class 11
Maths
Calculus
Continuity And Differentiability
Let
f
(
x
)
=
⎩
⎪
⎨
⎪
⎧
n
→
∞
lim
(
4
c
o
t
(
π
x
)
)
n
+
1
a
x
(
x
−
1
)
(
4
c
o
t
(
π
x
)
)
n
+
(
p
x
2
+
2
)
,
x
∈
(
0
,
1
)
∪
(
1
,
2
)
and
0
,
x
=
1
If f(x) is differentiable for all
x
∈
(
0
,
2
)
then
(
a
2
+
p
2
)
equals
1
2
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class 11
| maths
| continuity and differentiability
Solutions for all the questions from class 11
of subject maths
of chapter continuity and differentiability
Filter Results
CLASS
class 10
class 11
class 12
class 6
class 7
class 8
class 9
SUBJECT
maths
CHAPTER
application of derivatives
application of integrals
binomial theorem
circle
circles
complex numbers
complex numbers and quadratic equations
continuity and differentiability
coordinate geometry
daily practice problems
View All ↓
Class 11
Maths
Calculus
Continuity And Differentiability
If
y
=
e
−
x
cos
x
a
n
d
y
n
+
k
n
y
=
0
,
w
h
e
r
e
y
n
=
d
x
n
d
n
y
a
n
d
k
n
are constants
∀
n
∈
N
,
then (a)
k
4
=
4
(b)
k
8
=
−
1
6
(c)
k
1
2
=
2
0
(d)
k
1
6
=
−
2
4
Class 11
Maths
Calculus
Continuity And Differentiability
Let
g
(
x
)
=
f
(
x
)
sin
x
,
w
h
e
r
e
f
(
x
)
is a twice differentiable function on
(
−
∞
,
∞
)
such that
f
(
−
π
)
=
1
.
The value of
∣
∣
∣
g
−
π
∣
∣
∣
equals __________
Class 11
Maths
Calculus
Continuity And Differentiability
If
y
=
2
x
2
+
2
1
x
x
2
+
1
+
(
lo
g
)
e
x
+
x
2
+
1
, prove that
2
y
=
x
y
p
r
i
m
e
+
(
lo
g
)
e
y
p
r
i
m
e
,
w
h
e
r
e
y
′
denotes the derivative w.r.t
x
˙
Class 11
Maths
Calculus
Continuity And Differentiability
If
y
=
x
(
l
o
g
x
)
log
(
l
o
g
x
˙
)
,
t
h
e
n
d
x
d
y
i
s
(a)
x
y
(
1
n
x
∞
x
−
1
)
+
2
1
n
x
1
n
(
1
n
x
)
)
(b)
x
y
(
lo
g
x
)
log
(
l
o
g
x
)
(
2
lo
g
(
lo
g
x
)
+
1
)
(c)
x
1
n
x
y
[
(
1
n
x
)
2
+
2
1
n
(
1
n
x
)
]
(d)
x
y
lo
g
x
lo
g
y
[
2
lo
g
(
lo
g
x
)
+
1
]
Class 11
Maths
Calculus
Continuity And Differentiability
A nonzero polynomial with real coefficient has the property that
f
(
x
)
=
f
p
r
i
m
e
(
x
)
f
˙
p
r
i
m
e
p
r
i
m
e
(
x
)
˙
If
a
is the leading coefficient of
f
(
x
)
,
then the value of
2
a
1
is____
Class 11
Maths
Calculus
Continuity And Differentiability
Let
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
2
x
y
−
1
for all real
x
a
n
d
y
and
f
(
x
)
be a differentiable function. If
f
p
r
i
m
e
(
0
)
=
cos
α
,
the prove that
f
(
x
)
>
0
∀
x
∈
R
˙
Class 11
Maths
Calculus
Continuity And Differentiability
(
lim
)
x
0
sin
(
x
c
)
x
a
sin
b
x
, where a , b , c in R ~{0},exists and has non-zero value. Then,
a
+
c
= (a) b (b)
−
1
0
(d) none of these
Class 11
Maths
Calculus
Continuity And Differentiability
If
f
(
x
)
=
{
sin
x
2
x
=
n
π
and
n
∈
I
2
x
=
n
π
and
g
(
x
)
=
⎩
⎪
⎨
⎪
⎧
x
2
+
1
4
5
x
=
0
x
=
0
x
=
2
then
x
→
0
lim
g
{
f
(
x
)
}
is
Class 11
Maths
Calculus
Continuity And Differentiability
If
x
=
t
2
,
y
=
t
3
,
t
h
e
n
d
x
2
d
2
y
=
(a)
2
3
(b)
(
4
t
)
3
(c)
2
(
t
)
3
(d)
2
3
t
Class 11
Maths
Calculus
Continuity And Differentiability
Let
f
(
x
)
=
⎩
⎪
⎨
⎪
⎧
n
→
∞
lim
(
4
c
o
t
(
π
x
)
)
n
+
1
a
x
(
x
−
1
)
(
4
c
o
t
(
π
x
)
)
n
+
(
p
x
2
+
2
)
,
x
∈
(
0
,
1
)
∪
(
1
,
2
)
and
0
,
x
=
1
If f(x) is differentiable for all
x
∈
(
0
,
2
)
then
(
a
2
+
p
2
)
equals
1
2
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page
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