Mathematics

Problem

Consider the function

h(x)=\begin{cases}\dfrac{1}{x-2}, & 2<x\le5,\\0, & x=2.\end{cases}

Which one of the following statements about the continuity of

h

[2,5]

is correct? a)

h

is continuous on

(2,5)

but discontinuous at both

x=2

and

x=5

. b)

h

is continuous on

(2,5]

but not at

x=2

. c)

h

is continuous at

x=2

but discontinuous at

x=5

. d)

h

is continuous on

[2,5]