Mathematics

Problem

Let

g(x)=\dfrac{\sin x}{x}

for

x\neq0

. a. (i) State the values of

x

for which

g(x)

is defined. b. (ii) Explain, with reason, whether the derivative

g'(x)

exists at

x=0

. c. (iii) Hence determine the domain of

g'(x)

. Give your answer in interval notation.