suppose f : E in R and p is a limit point of E if lim x-> p f (x)=0 and f (x)> 0 for all x in E then prove that lim x-> p 1/f (x)= infinity Solution We are given that lim x --> p f(x) = 0 So, lim x ---> p of (1/f(x)) = 1/0 = +/- infinity But we are given that f(x) > 0 for all x in E Therefore, the limit cannot be -infinity Therefore, lim x --> p of (1/f(x)) equals +INFINITY Hencr proved!.