- #1
Carl140
- 49
- 0
Homework Statement
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.
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?