The function g(x)=x−2x2−5x+6 is undefined at x=2. Which statement is most accurate regarding x→2limg(x)?
a) The limit exists and equals 0 since the numerator becomes zero at x=2. (Cancelling is unnecessary)
b) The limit does not exist because the function is undefined at x=2. (No value implies no limit)
c) The limit exists and equals −1 because, after cancelling the common factor, the expression becomes x−3. (Correct)
d) The limit is infinite because the denominator tends to zero more rapidly than the numerator near x=2. (Vertical asymptote)