Which statement best explains why x→3limx−3x3−27 exists and is finite?
a) Since both numerator and denominator approach 0, the limit must be 0 by direct substitution.
b) The limit cannot exist because the original expression is undefined at x=3.
c) Because the numerator contains the factor (x−3), the expression can be simplified to a polynomial that is continuous at x=3, so the limit is finite.
d) The denominator approaches 0 faster than the numerator, so the quotient grows without bound; therefore the limit is unbounded.