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Answers
Answer:
k=6
Step-by-step explanation:
MATHS
Find the value of K if f(x) is continuous at x=
2
π
,
f(x)=
⎩
⎪
⎨
⎪
⎧
π−2x
K.cosx
,ifx
=
2
π
3ifx=
2
π
December 27, 2019avatar
Nizam Bhargava
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ANSWER
Given that function is continous at x=
2
π
f is continuous at x=
2
π
if L.H.L=R.H.L=f(
2
π
)
L.H.L
=
x→
2
π
−
lim
f(x)
=
x→
2
π
−
lim
π−2x
kcosx
=
x→
2
π
−
lim
2(
2
π
−x)
ksin(
2
π
−x)
=
2
k
x→
2
π
−
lim
(
2
π
−x)
sin(
2
π
−x)
Let y=
2
π
−x as x→
2
π
y→
2
π
−
2
π
y→0
So our equation becomes
=
2
k
y→0
lim
y
siny
=
2
k
×1=
2
k
R.H.L=
x→
2
π
+
lim
f(x)
=
x→
2
π
+
lim
π−2x
kcosx
=
x→
2
π
+
lim
2(
2
π
−x)
ksin(
2
π
−x)
=
2
k
x→
2
π
+
lim
(
2
π
−x)
sin(
2
π
−x)
Let y=
2
π
−x as x→
2
π
y→
2
π
−
2
π
y→0
So our equation becomes
=
2
k
y→0
lim
y
siny
=
2
k
×1=
2
k
Hence LHL=RHL=
2
k
Now,LHL=RHL=f(
2
π
)=3
⇒
2
k
=3
∴k=6