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Mathematics
Mathematics
Problem
If
f
(
x
)
=
x
−
e
x
+
cos
2
x
x
2
f(x) = \frac{x - e^x + \cos 2x}{x^2}
f
(
x
)
=
x
2
x
−
e
x
+
c
o
s
2
x
,
x
≠
0
x \ne 0
x
=
0
is continuous at
x
=
0
x = 0
x
=
0
, then where,
[
x
]
[x]
[
x
]
and
x
{x}
x
denote the greatest integer and fractional part function. a.
f
(
0
)
=
5
2
f(0) = \frac{5}{2}
f
(
0
)
=
2
5
b.
[
f
(
0
)
]
=
−
2
[f(0)] = -2
[
f
(
0
)]
=
−
2
c.
f
(
0
)
=
−
0.5
{f(0)} = -0.5
f
(
0
)
=
−
0.5
d.
[
f
(
0
)
]
⋅
f
(
0
)
=
−
1.5
[f(0)] \cdot {f(0)} = -1.5
[
f
(
0
)]
⋅
f
(
0
)
=
−
1.5
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