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Problems
If
f
(
x
)
=
{
sin
[
x
]
[
x
]
,
[
x
]
≠
0
0
,
[
x
]
=
0
f(x) = \begin{cases} \frac{\sin [x]}{[x]}, & [x] \neq 0 \\ 0, & [x] = 0 \end{cases}
f
(
x
)
=
{
[
x
]
s
i
n
[
x
]
,
0
,
[
x
]
=
0
[
x
]
=
0
w…
Problem
If
f
(
x
)
=
{
sin
[
x
]
[
x
]
,
[
x
]
≠
0
0
,
[
x
]
=
0
f(x) = \begin{cases} \frac{\sin [x]}{[x]}, & [x] \neq 0 \\ 0, & [x] = 0 \end{cases}
f
(
x
)
=
{
[
x
]
s
i
n
[
x
]
,
0
,
[
x
]
=
0
[
x
]
=
0
where
[
⋅
]
[ \cdot ]
[
⋅
]
denotes the greatest integer less than or equal to
x
x
x
, then a.
lim
x
→
0
f
(
x
)
=
sin
1
\lim_{x \to 0} f(x) = \sin 1
lim
x
→
0
f
(
x
)
=
sin
1
b.
lim
x
→
0
+
f
(
x
)
=
0
\lim_{x \to 0^+} f(x) = 0
lim
x
→
0
+
f
(
x
)
=
0
c. limit does not exist at
x
=
0
x=0
x
=
0
d. limit exists at
x
=
0
x=0
x
=
0
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