Let and be real numbers

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

Problem

Let

a

and

b

be real numbers. Consider the rational function

f(x)=\frac{(2a-1)x^{4}+bx^{3}+5}{(a+3)x^{4}+4x^{2}-1}.

(i) Determine, in terms of

a

and

b

, the value of

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

. (ii) If the limit equals

5

, obtain a relation between

a

and

b

. (iii) Given further that the limit in part (i) is finite, find all ordered pairs

(a,b)

satisfying both conditions.