The function is undefined at

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The function

g(x)=\dfrac{x^{2}-5x+6}{x-2}

is undefined at

x=2

. Which statement is most accurate regarding

\displaystyle \lim_{x\to2} g(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)