Rational functions often approach a finite limit as becomes very large
MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
Rational functions often approach a finite limit as x becomes very large, yet this behavior is not always immediately obvious from the full algebraic expression.
Consider the function
f(x)=5x3−7x+43x3+2x−1.
(1) Part (a) — Prediction and justification
(2) Part (b) — General explanation for polynomials of equal degree