Mathematics

Mathematics

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

at

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.

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