- #1
mscudder3
- 29
- 0
1. Let g_n (x)=nx*exp(-nx). Is the convergence uniform on [0, ∞)? On what subsets of [0,∞) is the convergence uniform?
3. I am looking for a proof of how the convergence is uniform (possibly using Weierstrass' M Test?). I understand that the subset that determines uniform convergence is none other than the radius of convergence. My attempt is applying the ratio test: R=lim(a_n / a_(n+1))= lim(n/(n+1) * exp(x))=exp(x). This is confusing to me since the radius of convergence should not depend on x.
3. I am looking for a proof of how the convergence is uniform (possibly using Weierstrass' M Test?). I understand that the subset that determines uniform convergence is none other than the radius of convergence. My attempt is applying the ratio test: R=lim(a_n / a_(n+1))= lim(n/(n+1) * exp(x))=exp(x). This is confusing to me since the radius of convergence should not depend on x.