Hi, I saw a proof/argument done today that I think was wrong:(adsbygoogle = window.adsbygoogle || []).push({});

It is finding the limit as a->oo of the integral from 0 to b<oo:

Int_(0..b) Sqr[x(1 +cos(ax))]dx , where Sqr is the square root

Now, the argument given was that one could find a bound for the oscillation

of (1+cos(ax)).

The problem I have is that, no matter what the trick may be, cos(ax) will take

values of 1 , and of -1 (at 2kPi and 2(k+1)Pi respectively; k an integer), so that

the value of the limit will go from:

i) 0 , when cos(ax)=-1 , to:

ii) Int_

(0..b) Sqr[2x]dx =(Sqr2)x^(-1/2), which is an improper integral at x=0, but does not

go to zero.

So the limit does _not_ exist, right?

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# Existence of Limit with Integrals.

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