Let f(x)= { sinx/x +cosx, x not equal to 0 2, x=0. Show that f(x) is continuous at x=0. Share with your friends Share 5 Varun.Rawat answered this LHL = limx→0- fx = limx→0- sin xx + cos xPut x = 0-h, as x→0-, then h→0LHL = limh→0sin0-h0-h + cos0-h=limh→0- sin h-h + cos h=limh→0sin hh + cos h=1 + cos 0=1 + 1=2RHL = limx→0+ fx = limx→0+ sin xx + cos xPut x = 0+h, as x→0+, then h→0LHL = limh→0sin0+h0+h + cos0+h=limh→0sin hh + cos h=1 + cos 0=1 + 1=2Now, f0 = 2Since, LHL = RHL = f0So, f is continuous at x = 0 4 View Full Answer Manthan answered this when limit tends zero sin x/x will be equal to 1 and cosx equals 1 , thus LHL = RHL as limit exits .therefore function is continuos at x=0. to make things easier draw graph 2
