Let fn(x)=sin(nx)nf_n(x) = \frac{\sin(nx)}{\sqrt{n}}fn(x)=nsin(nx) for x∈[0,π]x \in [0, \pi]x∈[0,π]. Which statement is correct?
fnf_nfn converges uniformly to 000 on [0,π][0, \pi][0,π].
fnf_nfn converges pointwise to ∞\infty∞.
fnf_nfn does not converge pointwise.
fnf_nfn converges uniformly to sin(x)\sin(x)sin(x).