Let . Which of the following statements best explains why…
MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
Let g(x)=x2−13x+5. Which of the following statements best explains why x→∞limg(x)=0?
(a) Because the leading coefficient of the numerator is less than the leading coefficient of the denominator, the fraction approaches zero.
(b) Because cancelling an x from top and bottom leaves x−13, which goes to 0 as x becomes large.
(c) Because the degree of the denominator is greater than the degree of the numerator, the value of the fraction becomes arbitrarily small for large x.
(d) Because the constant term −1 in the denominator forces the entire denominator to grow negatively without bound, the fraction approaches zero.