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Byju's Answer
Standard XII
Mathematics
Higher Order Derivatives
Find the valu...
Question
Find the value of
K
if
f
(
x
)
is continuous at
x
=
π
2
,
f
(
x
)
=
⎧
⎪ ⎪
⎨
⎪ ⎪
⎩
K
.
cos
x
π
−
2
x
,
i
f
x
≠
π
2
3
i
f
x
=
π
2
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Solution
Given that function is continous at
x
=
π
2
f
is continuous at
x
=
π
2
if L.H.L
=
R.H.L
=
f
(
π
2
)
L.H.L
=
lim
x
→
π
2
−
f
(
x
)
=
lim
x
→
π
2
−
k
cos
x
π
−
2
x
=
lim
x
→
π
2
−
k
sin
(
π
2
−
x
)
2
(
π
2
−
x
)
=
k
2
lim
x
→
π
2
−
sin
(
π
2
−
x
)
(
π
2
−
x
)
Let
y
=
π
2
−
x
as
x
→
π
2
y
→
π
2
−
π
2
y
→
0
So our equation becomes
=
k
2
lim
y
→
0
sin
y
y
=
k
2
×
1
=
k
2
R.H.L
=
lim
x
→
π
2
+
f
(
x
)
=
lim
x
→
π
2
+
k
cos
x
π
−
2
x
=
lim
x
→
π
2
+
k
sin
(
π
2
−
x
)
2
(
π
2
−
x
)
=
k
2
lim
x
→
π
2
+
sin
(
π
2
−
x
)
(
π
2
−
x
)
Let
y
=
π
2
−
x
as
x
→
π
2
y
→
π
2
−
π
2
y
→
0
So our equation becomes
=
k
2
lim
y
→
0
sin
y
y
=
k
2
×
1
=
k
2
Hence LHL
=
RHL
=
k
2
Now,LHL
=
RHL
=
f
(
π
2
)
=
3
⇒
k
2
=
3
∴
k
=
6
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1
Similar questions
Q.
Find the value of
k
is continuous at
x
=
π
2
, where
f
(
x
)
=
⎧
⎪ ⎪
⎨
⎪ ⎪
⎩
k
cos
x
π
−
2
x
,
if
x
≠
π
2
3
,
if
x
=
π
2
Q.
Determine the value of
k
if
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
Q.
Let
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
1
−
sin
3
x
3
cos
2
x
,
i
f
x
<
π
2
a
,
i
f
x
=
π
2
b
(
1
−
sin
x
)
(
π
−
2
x
)
2
,
i
f
x
>
π
2
. If
f
(
x
)
is continuous at
x
=
π
2
, find
a
and
b
.
Q.
Find the value of k if f(x) is continuous at x = π/2, where
f
x
=
k
cos
x
π
-
2
x
,
x
≠
π
/
2
3
,
x
=
π
/
2
Q.
If
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
1
−
sin
3
x
3
cos
2
x
,
if
x
<
π
2
a
,
if
x
=
π
2
b
(
1
−
sin
x
)
(
π
−
2
x
)
2
,
if
x
>
π
2
so that
f
(
x
)
is continuous at
x
=
π
2
, then
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