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Byju's Answer
Standard XII
Mathematics
Continuity of a Function
Determine the...
Question
Determine the values of
a
,
b
,
c
for which
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
f
(
x
)
=
sin
(
a
+
1
)
x
+
sin
x
x
for
x
<
0
=
c
for
x
=
0
(
x
+
b
x
2
)
1
2
−
x
1
2
b
x
1
2
for
x
>
0
is continuous at
x
=
0
.
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Solution
c
=
lim
x
→
0
−
2
sin
(
a
+
1
)
x
+
sin
x
x
=
lim
x
→
0
−
2
sin
(
a
2
x
+
x
)
cos
a
2
x
x
=
a
+
2
c
=
lim
x
→
0
+
(
x
+
b
x
2
)
1
/
2
−
x
1
/
2
b
x
1
/
2
=
lim
x
→
0
−
(
1
+
b
x
)
1
/
2
−
1
b
=
0
f
(
x
)
is continuous at
x
=
0
⟹
a
+
2
=
0
⟹
a
=
−
2
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0
Similar questions
Q.
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
(
x
+
b
x
2
)
1
/
2
−
x
1
/
2
b
x
3
/
2
x
>
0
c
x
=
0
sin
(
a
+
1
)
x
+
sin
x
x
x
<
0
is continuous at
x
=
0
, then
Q.
Determine the values of
a
,
b
,
c
for which the function defined by
f
(
x
)
=
sin
(
a
+
1
)
x
+
sin
x
x
,
f
o
r
x
<
0
c
,
f
o
r
x
=
0
=
(
x
+
b
x
)
1
/
2
−
x
1
/
2
b
x
1
/
2
,
f
o
r
x
>
0
Is continuous at
x
=
0
Q.
Determine the values of
a
,
b
,
c
for which the function
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
sin
(
a
+
1
)
x
+
sin
x
x
f
o
r
x
<
0
=
c
f
o
r
x
=
0
=
(
x
+
b
x
2
)
1
/
2
−
x
1
/
2
b
x
3
/
2
f
o
r
x
>
0
is continuous at
x
=
0
.
Q.
the function f(x) =
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
s
i
n
(
a
+
1
)
x
+
s
i
n
x
x
f
o
r
x
<
0
c
f
o
r
x
=
0
(
x
+
b
x
2
)
1
/
2
−
x
1
/
2
b
x
3
/
2
f
o
r
x
>
0
, is continuous at x = 0, the a,b,c should satisfy
Q.
Determine the values of a, b, c for which the function
f
x
=
sin
(
a
+
1
)
x
+
sin
x
x
,
for
x
<
0
c
,
for
x
=
0
x
+
b
x
2
-
x
b
x
3
/
2
,
for
x
>
0
is continuous at x = 0.
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