Show g(x)>=f(x)>=0 for f(x)=(1-cosx)/x, g(x)=2/x

Limits, differentiation, related rates, integration, trig integrals, etc.
jdom543
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Show g(x)>=f(x)>=0 for f(x)=(1-cosx)/x, g(x)=2/x

Postby jdom543 » Sat Sep 04, 2010 3:01 pm

and Interval:

Show that

How do I do that?

nona.m.nona
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Postby nona.m.nona » Sat Sep 04, 2010 9:47 pm

jdom543 wrote: and Interval:

Show that

For f(x): What do you know about the value of the cosine? Then what does this tell you about the value (and sign) of 1 - cos(x)? Given that x is always positive, what then do you know about the value of f(x)?

For g(x): The denominators are always the same, so you need only compare the numerators. What is the maximum value of the numerator of f(x)? How does this compare with the constant value of the numerator of g(x)?


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