Provide an appropriate response.Plot the functions u(x) = 7, l(x) = 7 - x2, and f(x) = 6 + . Then use these graphs along with the Squeeze Theorem to prove that f(x) = 7 .

Question

What will be an ideal response?

Answer 1

From the graph, it can be seen that the graph of f(x) = 6 +  is between the graphs of l(x) = 7 - x² and u(x) = 7. Also l(x) = 7 and u(x) = 7. Since the graph of f(x) = 6 +  is squeezed between the graphs of l(x) = 7 - x² and u(x) = 7, both of which go to 7 as x?0, by the Squeeze Theorem we can conclude that f(x) = 7.