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

What will be an ideal response?



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

Mathematics

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Mathematics