For each of the following rational functions

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

For each of the following rational functions, determine the limits indicated and justify your answer clearly. (i)

f(x)=\dfrac{7x^{4}-5x+9}{2x^{6}+3}

(ii)

g(x)=\dfrac{-5x^{3}+11x-8}{x^{3}-4x^{2}+2}

(iii)

h(x)=\dfrac{3x^{5}-4x^{2}+1}{-2x^{2}+7}

For every function above: (a) Find

\displaystyle \lim_{x\to\infty}

of the function. (b) Find

\displaystyle \lim_{x\to -\infty}

of the function. (c) If the limit is infinite, specify whether it is

+\infty

-\infty

and explain how the signs of the leading terms determine your conclusion.