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 .
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A. (0.4, 5.8) B. (2, 5.8) C. (-0.4, 5.8) D. (-0.4, 4.2)
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Evaluate the integral using integration by parts with the indicated choices of u and dv.