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.