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Mathematics
Problem
Let
g
(
x
)
=
e
3
x
+
5
x
2
2
e
3
x
−
x
5
g(x)=\dfrac{e^{3x}+5x^{2}}{2e^{3x}-x^{5}}
g
(
x
)
=
2
e
3
x
−
x
5
e
3
x
+
5
x
2
. Answer the following questions. a. (i) Find
lim
x
→
∞
g
(
x
)
\displaystyle \lim_{x\to\infty} g(x)
x
→
∞
lim
g
(
x
)
. b. (ii) For sufficiently large positive
x
x
x
, will
g
(
x
)
g(x)
g
(
x
)
ever take a negative value? Give justification based on your result in part (i).
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