Mathematics

Problem

a. Consider the function

h(x)=\begin{cases}\dfrac{x^{2}-4}{x-2},& x\ne2,\\k,& x=2.\end{cases}

Find the value of

k

that makes

h(x)

continuous at

x=2

. b. If any other value of

k

is chosen, state the type of discontinuity that remains at

x=2

. a. Consider the function

h(x)=\begin{cases}\dfrac{x^{2}-4}{x-2},& x\ne2,\\k,& x=2.\end{cases}

Find the value of

k

that makes

h(x)

continuous at

x=2

. b. If any other value of

k

is chosen, state the type of discontinuity that remains at

x=2