Mathematics

Problem

A function

h

is defined by

h(x)=\frac{x^{2}-4}{x-2}.

The graph of

h

has a removable discontinuity at

x=2

. (a) Determine the domain of

h

and express your answer in interval notation. (b) Explain whether

h

is differentiable at

x=2

. Include a discussion of the relationship between differentiability and continuity at that point. (c) A new function

k

is defined by

k(x)=h(x)

for

x\neq2

and

k(2)=4

. Determine whether

k

is differentiable at

x=2

. Justify your conclusion.