Mathematics

Problem

Consider the rational function

F(x)=\frac{(2x-3)(x^{2}+1)(x+4)}{(x-5)(-3x^{2}+2)}.

(a) Determine the degree of the numerator and the degree of the denominator. (b) Find

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

, showing all necessary steps. (c) Find

\displaystyle \lim_{x\to -\infty} F(x)

and explain carefully how the signs of the leading terms influence the result. (d) Using your answers to parts (b) and (c), state the equation(s) of any horizontal asymptote(s) of the graph of

y=F(x)

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