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Mathematics
Mathematics
Problem
Suppose
lim
x
→
2
p
(
x
)
=
5
\lim_{x\to 2}p(x)=5
lim
x
→
2
p
(
x
)
=
5
and
lim
x
→
2
q
(
x
)
=
−
3
\lim_{x\to 2}q(x)=-3
lim
x
→
2
q
(
x
)
=
−
3
. Which one of the following statements is always true? a)
lim
x
→
2
[
p
(
x
)
+
q
(
x
)
]
=
2
\displaystyle\lim_{x\to 2}[p(x)+q(x)]=2
x
→
2
lim
[
p
(
x
)
+
q
(
x
)]
=
2
b)
lim
x
→
2
[
p
(
x
)
−
q
(
x
)
]
=
2
\displaystyle\lim_{x\to 2}[p(x)-q(x)]=2
x
→
2
lim
[
p
(
x
)
−
q
(
x
)]
=
2
c)
lim
x
→
2
p
(
x
)
q
(
x
)
=
−
15
\displaystyle\lim_{x\to 2}\dfrac{p(x)}{q(x)}=-15
x
→
2
lim
q
(
x
)
p
(
x
)
=
−
15
d)
lim
x
→
2
[
p
(
x
)
+
q
(
x
)
]
=
8
\displaystyle\lim_{x\to 2}[p(x)+q(x)]=8
x
→
2
lim
[
p
(
x
)
+
q
(
x
)]
=
8
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