#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.#