(a) State the relationship between the degrees of the numerator and the denominator…
MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
(a) State the relationship between the degrees of the numerator and the denominator of a rational function that determines whether its limit as x→∞ is 0, a non–zero constant, or unbounded.
(b) Give a brief justification (no numerical example necessary) for why a rational function whose numerator has lower degree than its denominator approaches 0 as x→∞.
(c) Consider the function f(x)=2x2+3x−45x2−7. Without performing long division or L’Hospital’s Rule, describe the value that f(x) approaches as x becomes very large, and interpret this result as a horizontal tendency of the graph.