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Byju's Answer
Standard XII
Mathematics
Continuity in an Interval
If fx= x 2 ...
Question
If
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
x
2
a
;
0
≤
x
<
1
−
1
;
1
≤
x
<
√
2
2
b
2
−
4
b
x
2
;
√
2
≤
x
<
∞
then find the value of
a
and
b
if
f
(
x
)
is continuous in
[
0
,
∞
)
.Find
a
+
b
.
Open in App
Solution
Given
f
(
x
)
is continuous
Apply continuity at
x
=
1
We get
1
a
=
−
1
, so the value of
a
is
−
1
.
Apply continuity at
x
=
√
2
We get
−
1
=
b
(
b
−
2
)
So the value of
b
is
1
.
∴
a
+
b
=
−
1
+
1
=
0
Suggest Corrections
0
Similar questions
Q.
Let
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
x
2
a
;
0
≤
x
<
1
a
;
1
≤
x
<
√
2
2
b
2
−
4
b
x
2
;
√
2
≤
x
<
∞
If
f
(
x
)
is continuous for
0
≤
x
<
∞
, then the most suitable values of
a
and
b
are
Q.
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
Q.
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
Q.
Given
f
(
x
)
=
x
2
+
a
, if
x
≤
0
=
2
√
1
+
x
2
+
b
, if
x
>
0
and
f
(
−
1
)
=
2
, if
f
is continuous at
x
=
0
, then
(
a
,
b
)
≡
____
Q.
f
(
x
)
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
e
x
−
1
+
a
x
x
2
,
x
>
0
b
x
=
0
sin
x
2
x
x
<
0
find
a
+
b
if
f
(
x
)
is continuous at
x
=
0
.
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