Ok

the functions f(x) and g(x) are defined by the formulae

f(x) = sin 1/x g(x) = x sin 1/x for x does not equal 0

f(0) = g(0) = 0

(b) Give the values of limx-->0 f(x) and limx-->0 g(x), if they exist, with brief reasons for your answers.

(c) Which of the functions f(x) and g(x) is continuous at x = 0?

(d) use the difference quotient (g(x) - g(0))/x-0 to show that g(x) is not differentiable at x = 0

(e) Use a difference quotient to show that the function h(x) defined by h(x) = x^2 sin 1/x for x (does not equal) 0 and h(0) = 0 is differentiable at x = 0

(f) Use the substitution u = 1/x to evaluate limx-->[infinity] g(x)