Mathematics

Problem

Which of the following best describes the discontinuity of the function

f(x)=\frac{x^{2}-9}{x-3}

x=3

? a) No discontinuity; the function is continuous at

x=3

since the factor

(x-3)

cancels. b) A removable discontinuity because

\displaystyle\lim_{x\to3}f(x)

exists while

f(3)

is undefined. c) A jump discontinuity because the one-sided limits at

x=3

are not equal. d) An infinite discontinuity because

f(x)

grows without bound as

x

approaches 3.