Find the value of k for which the function f is defined as: f(x)={1-cos4x/8x2, x not equal to 0 k, x=0 is continuous at x=0. Share with your friends Share 2 Varun.Rawat answered this LHL = limx→0- fx = limx→0- 1 - cos 4x8x2Put x = 0-h; as x→0-, then h→0LHL = limh→0 1 - cos 40-h80-h2=limh→01 - cos 4h8h2=limh→02 sin22h8h2=14limh→0 sin 2hh × limh→0 sin 2hh=14limh→0 sin 2h2h×2 × limh→0 sin 2h2h×2=14×1×2×1×2=1RHL = limx→0+ fx = limx→0+ 1 - cos 4x8x2Put x = 0+h; as x→0+, then h→0RHL = limh→0 1 - cos 40+h80+h2=limh→01 - cos 4h8h2=limh→02 sin22h8h2=14limh→0 sin 2hh × limh→0 sin 2hh==14limh→0 sin 2h2h×2 × limh→0 sin 2h2h×2=14×1×2×1×2=1Now, f0 = kSince, f is continuous at x = 0, thenLHL = RHL = f0⇒1 = 1 = k⇒k = 1 15 View Full Answer
