Let be defined by for

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

Problem

Let

h

be defined by

h(x)=\dfrac{x^{2}-9}{x-3}

for

x\neq 3

. The value

h(3)

is not defined. Determine the type of discontinuity of

h

x=3

. (a) Jump discontinuity, because the one-sided limits are finite but unequal. (b) No discontinuity, because the expression simplifies to

x+3

for all

x

. (c) Removable discontinuity, because the limit exists and is finite. (d) Infinite discontinuity, because

h(x)

diverges to

\infty

near

x=3