Mathematics

Problem

Consider the rational function

p(x)=\dfrac{x^{4}+px^{3}+q}{(2-p)x^{4}+5}

, where

p

and

q

are real numbers. (a) Determine all real values of

p

for which

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

exists and is finite. (b) For each value of

p

obtained in part (a), evaluate the finite limit found in part (a). (c) Explain why the limit does not exist or is unbounded for values of

p

not included in your answer to part (a).