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AMU Engineering 2020 solved paper Solved Paper
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© examsnet.com
Question : 146
Total: 150
If
[
⋅
]
denotes the greatest integer function, then
f
(
x
)
=
[
x
]
+
[
x
+
1
2
]
is continuous at
x
=
1
2
is discontinuous at
x
=
1
2
lim
x
→
1
2
+
f
(
x
)
=
2
lim
x
→
1
−
2
f
(
x
)
=
1
Validate
Solution:
We have,
f
(
x
)
=
[
x
]
+
[
x
+
1
2
]
Clearly,
f
(
x
)
is discontinuous at
x
=
1
2
Also,
lim
x
→
1
−
2
f
(
x
)
=
0
and
lim
x
→
1
2
+
f
(
x
)
=
1
© examsnet.com
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