suppose that lim x^2*f(x)=L.  Show that lim f(x)=0
              x>infinity                x>infinity

Given lim x^2*f(x)=L as x approaches infinity.

This can be separated into (lim x^2 as x approaches infinity) * (lim
f(x) as x approaches infinity).

For this limit to evaluate to a constant integer, the function f(x)
must be a multiple of x^-2. For example, if f(x) = 5x^-2, then the
limit would be 5.

Any multiple of this function, x^-2, has a limit of 0 as x approaches
infinity.  Therefore, the limit as x approaches inifinity of f(x) must
be 0.

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before you rate it.

Thanks,
chis-ga