Does converges pointwise or uniformly as k approaches infinity?
Isn't the limit 0?
there is also a theorem that has to do with the derivative being bounded implies uniform convergence (or maybe it's uniform convergence implies the derivative is bounded. i can never remember which. i should look it up)
Not sure if this argument is good or not. I think it converges to the zero function. It's been a while since I studied calculus.
If we define the domain as the real line, then we know is bounded by and for all Let be in the domain. Given , there is some such that for all . Then