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Byju's Answer
Standard XII
Mathematics
Continuity of a Function
If fx=√2cos...
Question
If
f
(
x
)
=
√
2
cos
x
−
1
cot
x
−
1
,
x
≠
π
4
, find the value of
f
(
π
4
)
so that function f becomes continuous at
x
=
π
4
.
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Solution
f
(
x
)
=
√
2
cos
x
−
1
cot
+
x
−
1
f
(
π
4
)
=
2
f
(
x
)
=
√
2
cos
x
−
1
cos
x
sin
x
−
1
(
√
2
cos
z
−
1
)
sin
x
cos
x
−
sin
x
u
sin
g
L
h
o
s
p
i
t
a
l
r
u
l
e
=
√
2
sin
x
−
0
−
cos
e
c
x
=
√
2
sin
x
−
cos
e
c
2
x
f
(
π
4
)
=
√
2
sin
(
π
4
)
cos
e
c
2
(
π
4
)
=
√
2
×
1
√
2
(
√
2
)
2
1
2
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0
Similar questions
Q.
If
f
(
x
)
=
√
2
cos
x
−
1
cot
x
−
1
,
x
≠
π
4
then, find the value of
f
(
π
4
)
so that
f
(
x
)
becomes continuous at
x
=
π
4
Q.
The function
f
(
x
)
=
cos
x
−
sin
x
cos
2
x
is not defined at
x
=
π
4
The value of
f
(
π
4
)
so that
f
(
x
)
is continuous at
x
=
π
4
is
Q.
If
f
(
x
)
=
1
−
t
a
n
x
1
−
√
2
s
i
n
x
, for
x
≠
π
4
is continuous at
x
=
π
4
, find
f
(
π
4
)
Q.
If
f
(
x
)
=
tan
(
π
4
−
x
)
cos
2
x
for
x
≠
π
4
, then find the value which can be given to
f
(
x
)
at
x
=
π
4
so that the function becomes continuous every where in
(
0
,
π
/
2
)
Q.
If
f
x
=
tan
π
4
-
x
cot
2
x
for x ≠ π/4, find the value which can be assigned to f(x) at x = π/4 so that the function f(x) becomes continuous every where in [0, π/2].
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