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Manipal Entrance Test 2020 Math Paper
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© examsnet.com
Question : 5
Total: 70
If
f
(
x
)
=
{
sin
[
x
]
[
x
]
for
[
x
]
≠
0
0
for
[
x
]
=
0.
where,
[
x
]
denotes the greatest integer less than or equal to
x
, then
lim
x
→
0
f
(
x
)
is equal to
1
-1
0
Dose not exit
Validate
Solution:
Given,
f
(
x
)
=
{
sin
[
x
]
[
x
]
f
o
r
[
x
]
≠
0
0
f
o
r
[
x
]
=
0.
L
H
L
=
lim
x
→
0
−
f
(
x
)
=
lim
x
→
0
−
sin
(
1
+
[
x
]
)
[
x
]
=
sin
[
1
−
1
]
−
1
=
sin
0
−
1
=
0
R
H
L
=
lim
x
→
0
+
f
(
x
)
=
lim
x
→
0
+
sin
(
1
+
[
x
]
)
[
x
]
=
sin
(
1
+
0
)
0
=
∞
Hence, limit does not exist.
© examsnet.com
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