Provide an appropriate response.Plot the functions u(x) = , l(x) = -, and f(x) = x sin (1/x3). Then use these graphs along with the Squeeze Theorem to prove that f(x) = 0.

Question

What will be an ideal response?

Answer 1

From the graph, it can be seen that the graph of f(x) = x sin (1/x³) is between the graphs of l(x) = - and u(x) =  . Also  = 0 and (-) = 0. Since the graph of f(x) = x sin (1/x³) is squeezed between the graphs of l(x) = - and u(x) = , both of which go to 0 as x?0, by the Squeeze Theorem we can conclude that f(x) = 0 .