Let h(x)= cases x^ 2 -1 x-1 ,& x 1 2,& x=1 cases Which of the following is true about at ?

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

Problem

Let

h(x)=\begin{cases}\dfrac{x^{2}-1}{x-1},& x\neq1\\2,& x=1\end{cases}

Which of the following is true about

h

x=1

? (a)

h

is discontinuous at

x=1

because the limit equals

0

. (b)

h

is continuous at

x=1

because the limit equals

2

. (c)

h

is discontinuous at

x=1

because the limit equals

2

but

h(1)

is not defined. (d)

h

is continuous at

x=1

because

h(1)

is defined even though the limit does not exist.