Question #fb419

1 Answer
Jun 13, 2017

# 0.#

Explanation:

#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.#