Question #fb419

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Answer 1 · 2017-06-13T18:02:38

$0.$

$lim_(x to oo) x(2r^2-2r^2cos(360/x))$

$=lim_(x to oo) 2r^2x(1-cos(360/x))$

Now, $1-costheta=2sin^2(theta/2),$

$"The Reqd. Lim.="lim_(x to oo)2r^2x{2sin^2(180/x)},$

$=lim_(x to oo) 4r^2x{sin(180/x)}^2.$

Recall that, $lim_(theta to 0) sintheta/theta=1.$

$:." The Reqd. Lim.="lim_(x to oo) 4r^2x{sin(180/x)/(180/x)}^2(180/x)^2,$

$=(4r^2)(1)^2(180)^2lim_(x to oo) 1/x$

$=0.$