Let . Answer the following…

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

g(x)=\dfrac{e^{3x}+5x^{2}}{2e^{3x}-x^{5}}

. Answer the following questions. (i) Find

\displaystyle \lim_{x\to\infty} g(x)

. (ii) For sufficiently large positive

x

, will

g(x)

ever take a negative value? Give justification based on your result in part (i).