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Mathematics
Mathematics
Problem
Suppose
lim
x
→
2
f
(
x
)
=
3
\displaystyle \lim_{x\to 2} f(x)=3
x
→
2
lim
f
(
x
)
=
3
and
lim
x
→
2
g
(
x
)
=
0
\displaystyle \lim_{x\to 2} g(x)=0
x
→
2
lim
g
(
x
)
=
0
. Is the limit
lim
x
→
2
f
(
x
)
g
(
x
)
\displaystyle \lim_{x\to 2}\dfrac{f(x)}{g(x)}
x
→
2
lim
g
(
x
)
f
(
x
)
necessarily defined and finite? Give a brief reason for your answer.
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