1. The problem statement, all variables and given/known data Let f: [0,1] -> R (R-real numbers) be a continuous non constant function such that f(0)=f(1)=0. Let g_n be the function: x-> f(x^n) for each x in [0,1]. I'm trying to show that g_n converges pointwise to the zero function but NOT uniformly to the zero function. 3. The attempt at a solution I thought: sup |g_n(x) | = sup |f(x^n)| now if I can only show that this doesn't tends to zero then we are done but I can't. I also have no idea how to show it converges pointwise to zero. Can you please help?