Which of the following statements best explains why x→4limx−4x2−16=8?
a) Since (x2−16)=(x−4)2, cancelling one factor leaves (x−4), which approaches 0, so the limit is 0.
b) Because the factor x−4 is common to both numerator and denominator, cancelling it gives x+4, a polynomial that is continuous at x=4, so the limit is 8.
c) Because x−4x2−16 is defined at x=4, direct substitution gives 8.
d) Because a 0/0 limit can be evaluated by differentiating only the numerator; (x2−16)′x=4=8, so the limit is 8.