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Mathematics
Problem
Let
f
(
x
)
=
3
x
2
+
1
x
2
−
x
f(x)=\dfrac{3x^{2}+1}{x^{2}-x}
f
(
x
)
=
x
2
−
x
3
x
2
+
1
. For
ε
=
0.02
\varepsilon=0.02
ε
=
0.02
, determine the smallest integer
M
M
M
among the following choices such that
∣
f
(
x
)
−
3
∣
<
ε
|f(x)-3|<\varepsilon
∣
f
(
x
)
−
3∣
<
ε
whenever
x
>
M
x>M
x
>
M
. a)
150
150
150
b)
200
200
200
c)
152
152
152
d)
302
302
302
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