Evaluate the limits at infinity of each of the following rational functions and hence…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Evaluate the limits at infinity of each of the following rational functions and hence state whether the graph of the function approaches the

x

–axis, a horizontal line other than the

x

–axis, or becomes unbounded. (i)

f_{1}(x)=\dfrac{4x^{2}+9}{3x^{5}-2}

(ii)

f_{2}(x)=\dfrac{-7x^{3}+12x}{5x^{3}-x^{2}+1}

(iii)

f_{3}(x)=\dfrac{6-2x}{x^{2}+4}