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The area of the triangle having vertices...

The area of the triangle having vertices `(-2,1) , (2,1) ` and `lim_(m->oo)lim_(n->oo)cos^(2m)(n!pix)`; x is rational,`lim_(m->oo)lim_(n->oo)cos^(2m)(n!pix)`; where x is irrational) is:

Text Solution

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`n!pix`
`(1*2*3..n)pi(P/2)` is an integer
`cos^2(n!pix)=1`
where` cosnpi=(-1)^n`
`lim_(x->oo)cos^(2m)(n!pix)=1`
`n!pix` it not an integer
`0ltcos^2n!pix<1`
`lim_(x->oo)cos^(2m)n!pix=0`
...
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